->.-  1c 


University  of  California  •  Berkeley 


The  Theodore  P.  Hill  Collection 

0/ 

Early  American  Mathematics  Books 


9r^ 


'X9' 


4  f,  -  f//y. 


■^f      i4^>^,.V. 


9 


-r'^^'^'^^m^.mm 


A    KEW    SYSTEM     J' 


MERC  A  N  T I L  E    A  R I T II M  E  T I C ; 

ADAPTI'lD    TO     THE 

Commerce  of  tJje  ®nitetJ  &tztt^, 

IS      ITS 

DOMESTIC  AND  FOREIGN  RELATIONS; 

W  ITH 

FORMS    OF    ACCOUNTS,    AND    OTHER    V>RiTIXGS    U3l^\LLY 
OCCURRING  IN  TRADE. 


7ir  .yrCHJEL   WALSH,  A.  ]A. 


Iter  est  br*:i€  per  cranphh 


^?;^M 


ri^YVorcr,  (M^^s.^r^t^ 


"KtOY.y 


JanuariL  1806. 


^^^.:-.imS>. 


4 


RECOADIENDATIONS. 


Kexi:hiin/port,  May  1,   ISOO. 

AYR  the  subscribers  having  seen  Mr.  Walsh's  New  System 
of  MKUCANTILE  ARITHMETIC,  and  being  satisfied,  that 
it  is  better  calcuUited  than  any  yet  published,  to  fit  a  youth 
for  the  business  of  the  Compting-llouse,  cannot  but  wish  it  an 
extensive  circukition.  The  happy  elucidation  and  extended 
application  of  the  common  rules,  together  with  the  many  ori- 
ginal improvements,  while  they  accommplish  the  student  for 
commerce,  are  also  extremely  well  adapted  to  assist  and  inform 
the  merchant,  the  niaihier,  tiud  the  trader  in  their  various  oc- 
cupations. 


Dudley  A,  Tj/iigy 

FMnczcr  Stochcr, 
jnilia?}?  Bartlcr, 
Sarnnel  A.  Otls,jiin, 
'Dint ram  Co/Jin^ 


11  Hi  lam  IFjjer,  J:'}} , 
ilichard  Barf  let,  juu, 
WiUiam  W.  Proul, 
MicJiad  Li i lie. 


Boston,  May  \6tJi,  ISOO. 
^VE  the  subscribers,  having;  examined  INIr.  ^VALSlI*s  New 
System  of  MERCANTILE  ARirilMETIC,  and  being  per- 
suaded that  it  is  better  calculated  than  any  we  have  met  with, 
to  cpialify  young  men  for  admission  into  Compting- Houses,  we 
\\\A\  tlrat  it  may  have  an  extensive  circulation.  Ihc  clear  ex- 
.■ini'lilioation  and  pertinent  ap])]ication  of  .the  common  rules, 
logciher  with  the  many  useful  additions  and  improvements 
Mhich  it  contains,  will  render  it  extremely  useful  for  the  mer- 
chant, the  mariner,  and  all  the  other  trading  classes  of  society. 
Marsfon  }  I  at  son,  I       Jo/u?  l.owcll^jxtn, 

John  C  Jones,  J^pk  Jlussell, 

John  Codman,  .^Kbld  Welles,  jun, 

Stephen  lli^ginson,  \      '^^^han  Jackson, 


V 


) 


Sakni,  October  7 tlh   ISOO. 

V'W  t' c  rnl'f-.crihor?,   Merchants  cf  Salem,  convinced  of  the 
y\vvv  \'\^v\\vi^  the  terms  of  bii-iiiess,  the  value  of  coins, 

?A\\  ■-'   of  commerce,    more   familiar  to  the    United 

St;;trs  is  a  commercial  people,  do  approve  of  the  MERCAN- 
TiLI-:  MUTIlMlCriC  of  Mr.  Walsh,  and  recommend  it  as 
calculi;-  '  I  )  ouh^orvc  in  the  bcbt  manner  the  instruction  of  our 
youih,  ami  tl.c  purposes  of  a  well-informed  merchant. 


U'ni.  Gray,  ji/n. 
luiij.  Iiocigey, 


Jacob  Ashton^ 
Wm.  Prescot, 
Jacob  C rownin shield y 
Elias  Hasket  Derhy, 


^xtiut  t^  tlje  tijixh  €Utmx. 

X  HE  merit  of  Walsh's  INIkrca^tile  Arithmetic 
having  been  submitted  to  the  public,  and  Cbtablihlicd  by  tlic 
most  liberal  and  unequivocal  encouragement,  the  Editor  feels 
a  confidence  in  ofiering  a  third  Edition  of  twenty  thousand 
copies. 

It.  is  unnecessary  now  to  urge  tlic  superiority  of  this,  over 
every  similar  production  extant.  1  Le  disceriiment  of  men  of 
letters,  and  the  generous  spirit  of  a  commcrcitil  public  havr 
rendered  panegyric  useless  by  an  unprecedented  patronage.  In 
the  ver^r  short  period  of  its  exi>ten:'e  two  extcnsivo  imprcsi-ions 
liave  been  circulated  through  the  country,  and  orders  are  al- 
ready received  for  a  very  large  p:-oportion  of  the  third. 

The  value  of  any  work  must  be  decided  by  those  to  v.Iiom 
it  is  more  immediately  useful  ;  and  if  such  persons  pc:-sess  tl;c« 
means  of  discrimination  the  decision  will  undoubtedly  be  cor- 
rect. The  present  publication  is  adapted  as  well  to  assist  the 
researches  of  PJathematicians,  as  to  facilitate  the  negrci- 
ations  of  Merchants.  Such  characters  have  supported  it  by 
their  written  approbati')n,  and  recoiiimended  it  by  an  intrc^uc- 

lion  into  their  own  Sturlies  and  Cumrting  rooms.     ^  chools  ar. 
A2 


PREFACE. 

Academics  have  made  it  the  basis  of  a  mercantile  education, 
and  it  has  become  an  indispensable  assistant  to  every  trading 
class  of  the  community. 

This  impression  has  received  several  valuable  additions  under 
the  general  head  of  Exchange,  including  the  existing  exchange 
v.ith  Antwerp,  Trieste,  Genoa,  Venice,  Barcelona,  and  Pal- 
ermo in  Sicily,  and  many  useful  rules  under  each  of  these  par- 
ticular heads.  A  new  subject  is  likewise  added,  entitled 
*^  Arbitration  of  Exchange,''  the  importance  of  which 
v:i\\  easily  be  iseen  by  Merchants  whose  remittances  may  travel 
through  several  countries,  and  be  liable  to  the  rates  of  Exchange 
in  each. 

The  errors  of  the  last  edition  were  few  and  unimportant. 
"Hut  to  render  the  work  perfect,  they  have  been  minutely  con- 
sidered and  corrected. 

The  Editor  is  confident  that  the  present  edition  will  be  taken 
up  with  the  same  avidity  as  the  two  former,  and  he  assures  the 
public  that  the  work  shall  not  suffer,  cither  in  accuracy  of 
beauty,  by  the  liberality  of  its  patrons. 

EDMUND  M.  BLUNT. 

January,  1806. 


1^ 


CONTENTS, 


Numeration 13 

Simple   Addilion "^^i 

Subtraction 15 

Multiplication 15 

Division    .     ,     .     . i6 

Miscellaneous  Questions 19 

Table  of  Money,  Weights,  Measure?,  Sec 19 

Compound  Addition       .     .     .     .      , 23 

Subtraction        ...     - 26 

Practical  Questions  in  Compound  Addition  and  Subtraction     ...  28 

Reduction 21> 

To  find  the  contents  of  Grindstones* 33 

Reduction  of  American  Monies     .     .     .  • CA 

Compound  ]Muliiplicaticn         ...     * <li2 

Bills  of  Parcels '  .     .     .  48 

Compound  Division        , 40 

Decimal  Fractions 52 

Tables  of  Coins,  Wrights  niid  ?Joasures 61 

*  Tojiiid  the  valiis  sec  yage  69, 


Viij  CONTENTS. 

Page 

Tlie  Single  Hule  of  Three  Direct 64 

Inverse  Proportion 72 

Compound  Proportion         73 

Vulgar  Fractions 76 

Practice 88 

Tare  and  Tret *.     .     .     .  95 

Single   Fellowship 99 

Double  Fellowship         100 

Simple  Interest .,     .     .     , 101 

Kulc  established  by  the  Courts  of  Law  in  Massachusetts  for  making  up 
j«dgraents  on  securities  for  Money,  which  a-e  upon  interest,  and  on 

which  partial  payments  have  been  endorsed 116 

A  Table  shcAving  the  number  of  days,  from   any  d.iy  in  any  month  to 

tlie  snmc  day  in  any  other  month  tlirough  the  3'ear       .     ...     .     .  117 

Compound  Interest 118 

A  Table  shewing  the  amount  of  one  pound  or  one  dollar  for  any  num- 
ber of  years  under  33,  at  the  rates  of  5  and  6  per  cent,  per  annam, 

compound  interest 119 

Commission  and  Brokerage 121 

Insurance 123 

General  Average ^-t   . 

Buying  and  Selling  Stocks 1  25 

Discount ICr 

Bank  Discount 129 

Eq^iution  of  Payments        132 

P.vt.r 133 

Loss  and  Gain 1 .1.') 

A\]'i:.i\\ou  rJedial i:;8 

Alternate lo9 


COXTENTS.  ix 

Page 

Single  Poition         142 

l)c)ul)Ic  ro.i'.ioa 143 

Exchange  will)  Great-Britain        146 

Inlaiul .     .  1.50 

Huiuburgb 153 

Holland      .     .     .     , 159 

Denmark 1C3 

Bremen 'i65 

Antwerp •     .  16d 

Russia    *.*.....*«*••..  1^2 

ftmnQ        , , 170 

Tables  for  changing  Livres,.SoIs  and  Dcuiers,  to  Francs  and  Centimes  176 

Table  for  reducing  Francs  and  Centimes  to  Livres,  Sols  and  Deniers  177 

Exchange  with  Spain 17  8 

Barcelona 186 

Portugal 1C8 

Leghorn 190 

Naples         19.1 

Trieste 19i 

I*alcrmo  (in  Sicily^        195 

Genoa         193 

'\'eiiicc         /,..     .  199 

.•            .            Smyrna        200 

Jamaica  and  Bermudas  .     .     • 20 i 

Barbadocs        20:> 

Martinico,  Tobago  and  St.  Chrli>to[>!icr's      ....  20q 

French-  West- Indies 207 


,  CONTENTS.   ^  . 

Page 

Exchange  with  Si>anlsh  West-ladies 210 

Calcutta ^^^ 

Bombay ^^^ 

Madras ^^^ 

Batavia '  ^14 

China 2^^ 

Manilla ^^^ 

Ceylon         .     .     .     ' 218 

T  219 

Japan    

Tonnage  of  Goods  from  the  East-Indies  to  Europe        220 

Arbdratioii  of  Exchange 

Mode  of  calculating  American  Duties        S^-i 

Hates  at  which  all  foreign  coins  are  estimated  at  the  Custom-Houses  of 

the  United  States ^^^ 

nog 
Arithmetical  Progression        ..." 

'^'11 
Geometrical  ProgTession  

JV^rmutation *     ' 

E.vtracilon  of  the  Square  Ftoot ^"'^ 

of  the  Cube  Root         ^10 

of  the  Biqnadvate  Hoot  ^' ' '' 

General  TvulcfoF  Extracting  the  Roots  of  all  Powers ^'-i-^ 

Buodocimals        

contents  of  Bales,  Cases,  &c.   in  order  to  ascertain  the 

freight         ^^-^ 

To  fuid  ships'  tonnage  by  Carpenter's  measure --^^ 

the  Government  tonnage  of  ships ---^ 


CONTENTS.  XI 

Pag6 

Tables  of  Cordage         255 

for  receiving  and  pacing  Gold  Coins  of  France  and  Spain     .  257 

for  receiving  and  pacing  Gold  Coins  of  G.  Britain  and  Portugal  258 

Mercantile  Precedents 259 

Bill  of  Exchange 259 

Bill  of  Goods  at  an  advance  on  the  sterling  cost 259 

Promissory  Note      ...  v   j*. 260 

Beceipt  for  an  endorsement  on  a  Note      ........  260 

for  money  received  on  account 260 

Promissory  Note  by  two  persons        260 

General  Receipt 260 

Bill  of  Parcels 261 

Invoices .     ,     .     .  262 

Accounts  of  Sales * 264 

Accounts  Current     . 267 

Bill  of  Sale 271 

Interest  Account ,..,. 272 

Charter  Party ••.•.••...••  27^h 

Bill  of  Lading     ..•.•••,.•.,.,,..  274 


EXPLANATION 

OF  THE  CHARACrERS  USED  IN  THIS  WORK. 


:z:     SIGNIFIES  equality,  or  equal  to  :  as,  20  sliillingsizonc 
pound  :   that  is,  20  shillings  are  equal  to  1  pound. 

-I      Signifies  more,  or  Addition:  as  ()-f6zzl2,  that  is  6  ad- 
ded to  6'  is  equal  to  12. 

—     Signifies  less,  or  Subtraction  :  as,  6 — 2zz4,  that  is,  6  less 
2  IS  eqiuil  to  •!■. 

Sigindcs  Multiplication  ;  as,  6x2z=12  ;  that  is,  6  multi- 
plied I) J  2  is  equal  to  12. 

Si  -  •ifies  Division  ;  as   6-^2zz:o  ;  that  is  6  divided  b}'  2  is 
equal  to  3. 

Division  is   sometimes   expressed    byplacii-^;    i'  ^    niiml^ors 
fraction,  the  upper  figure  being  ti.  >  1,    and 

«cr  tlic  divisor  ;  thus,  ^^y^=:9  ;  tl;.  divided 

b^,  v^  .6  equal  to  9• 
;  :  :   :  Proportion  ;  as,  3  :  6  :  :  9  :  IS  ;  that  is,  as  three  is  to  6 
60  is  9  to  18. 

-v/     rr-:i\::,i  to  any  number   signiiios  tii^t  the  square  root  of 
i;,  re(;uired, 


MERCANTILE  ARITHMETia 


JniRITHMETIC  is  the  art  of  compiuing  by  numbers, 
^r\(\  has  five  principal  rules  tor  this  purpose,  viz.  Numeration^ 
Addition,  Subtraction,  Multiplication^  and  Diiision, 

KUMEllATION 

Tcachcth  to  express  any  proposed  mimbor  by  these  ten  clia- 
ractcrs,  O.  1.  2.  3.  4.  5.  6\  7.  8.  f).— O  is  called  a  cypher,  and 
•the  rest  figures  or  digits.  The  relative  value  of  which  depends 
upon  the  place  they  stand  in,  when  joined  together,  beginning 
at  the  right  hatid  as  in  tlK^.  following 

TABLE, 


<A 

'C 

C! 

£2 

o 

rj 

<n 

a 

o 

o 

V4 

o 

o 

:3 
o 

t/i 

a 

<n 

•5 

^ 

W3 

O 

G 

.2 

o 
CJ 

o 

in 

c: 

a 

♦1 

-a 

to 

o 

en 

y 

8 

7 

6 

5 

4 

3 

2 

1 

Though  the  table  consists  of  only  nine  places,  yet  it  may  be 
extended  to  more  places  at  pleasure  ;  as,  after  hundreds  of 
milhons,  read  thousands  of  millions,  ten  thoxisands  of  millions, 
hundred  thousands  of  millions,  then  miiHoHs  of  millions,  &c. 

TO  WRITE  NUMBERS, 

Rule.  Write  down  the  figures  as  their  values  ate  expressed., 
and  supply  any  dcticiency  in  Uie  order  with  cyphers. 


U  SIMPLE  ADDmON. 

Examples. 

Wrlic  down  in  proper  figures  tlio  following. niimbers. 

TwiMity-nir.e,  • 

Two  luindrod  and  forty-seven, 

Seven  thousand  nine  hundred  and  one, 

]'-igiity-four  thousand  three  hundred  and  twenty-nine, 

Nine  hundred  and  two  tho|j|and  six  hundred  and  tiftcen, 

Kigiity-nine  millions  and  nmcty, 

lour  millions  tour  hundred  thousand  and  forty, 

Nine  hundred  and  nine  millions  nine  hundred  and  ninctv. 

Seventy  millions  seventy  thousand  and  seventy. 

Eleven  thousand  eleven  hun-  Jourtcen  thousand  fourteen 

drcd  and  eleven.  hundred  and  fourteen. 

eleven  thousand  •  •  1  lOpO  fourteen  thousand  •  •  ]  4000 

e'even  hundred  •  •  •  •  3 100  fourteen  hundred  •  •    1400 

^  ieven 11  fourteen  •  •  •  • 14 


Total..  1 2111  Total..!  54  li 

To  express  in  zvords  any  numher  proposed  in  figures, 
KiTLE.  To  the  simple  value  of  each  figure,  join  the  name  of 
ace,  beginning   at  the  left  hand  and  reading  towards  tli« 
*  •'^'■'  ^^ 

Examples. 
Wiite  down  in  words  the  following  numbers* 

4^,      199,      2267,      S6693,      289732.,       ii9H9n. 
1169^90,         9919,       4320,         55OOO0IO. 


SIMPLBt  ADDITION 
Teacli£t!i  to 'collect  numbers  of  the  same  denominatian  intc 


Q.ne  sum. 

Examples, 

Gallon?:. 

Yards. 

Bushels. 

68965 

59473 

8754i>(j 

14753 

S9i4. 

17C9OO 

29684 

675 

574 

5769"^ 

29 

9 

171095 
171095 


SLMPLP.  SUBTRACTION.  i^ 


G.iHons. 

Y'dYih. 

RusIr'Is. 

1/573 

1  SOU  4- 1 

r.^ooia 

-iGS 

405).) 

31R9t 

57 

83 

:),  J 

9 

73'2t; 

7^^'^W 

As  tlK,'  lucrnintile  mctFiud  of  provlnir"  ad-iitloiv  In  to  reckon  downwards  a 
Wi'Il  ai  upwdrd^s  the  sums  uf  wUi;h  wiii  be  ciiual,  whi'U  l.htt  addilioi>  ib  j\u»i 
two  spaces  are  icit  f«r  the  work. 


SIMPLE  SUBTRACTION 

Tcachcth  to  take  a  less  number  from  a  greater  of  the  .same 
deaouiination;  and  thereby  to  shew  the  ditfcrence. 

Examples. 

Yards.  Gallons. 

From     5T46S532                  From  2p68914l 

'Jake      265S7491                  Take  I7i^3S76^ 


Rem.     30881041  Rem.       1175037S 


Proof    574()8532  Proof     i;^^6'8C)141 

3  fr^m  924357  take  565383  Rem.  35S974 

4  517684  Q^S72  2*25812 

5  510090  191939  318151 

6  191191  ^9^7  188234 

7  291619  ^W  !?90790 

8  500910  15723  485187 


SIMPLE  MULTIPLICATIOI^f 

Is  a  compendious  way  of  adding  numbers  of  the  same  name» 
'ihe  aumbei'  to  be  multiplied  is  called  the  multiplicand. 
'i  he  number  which  multiplies  is  called  ti>e  multiplier. 
The. number  arising  from  the  operation  is  called  the  produc: 


-OiPLK   iMULTIPLlCATiCxN. 


MUiriPLICATION  TABLB. 


1  r  '^ 

'5l    4       5 

Bj     7|     y 

.    i> 

10 

11      12 

-\     4 

6  1     8      10 

12  1  14- 1  16 

la 

20 

22        24 

.kj     6 

'9.\  12      15 

18      21  1  24 

27 

30 

33       .'6 

4f    ^ 

1  j.^  j  IQ     20 

f-  24  [  28     32 

-    o(> 

40 

44       4b 

;'.   ;   1.'' 

!n  1  20      26 

oO     Ao  I  40 

45 

50 

0.')        60 

,  24     30 

36  ^42     48 

o4  {    60 

66       72 

:  2«'j   ."5 

4T 

Ta  I  6d 

63  1     70- 

77        84 

21-.|32     40 

48 

56  1  d4 

72  -j     80 

88       V6 

)  t'7  \  b6  1  45 

54 

63  1  72 

81  1     90 

99     lOti 

i  SO     40     ^1 

60 

70     80- 

90  j  100 

110     120 

i  :-.;i    44    55 

66 

7?     88 

yp      1 10 

121      13 J 

;;^{>f  4B  16U 

TiJ 

•84     yd 

108     120 

132      144 

Examples. 

.ofiGOTd      5965468            47652:9-3 

6281947 

-ih/'T 

2 

3 

4 

11.930936            14295879 

25127788 

■  :u]t, 

26587  58  by         5 

product 

132Q37PO 

C)  67  437  2               6 

58046232 

7689657              7 

53827599 

2074876              9 

24073884 

4198543               10 

41985430 

7491685               11 

82408535 

26S94H9               12 

3227386<^ 

1768735             20 

35374700 

2vS914Q6         ^400 

115659840a 

5749857               7-8 

44S4S8S46. 

2653294          ~  872 

2313672368 

7.SU(i5987          ^893 

465346561391 

56-2916859 

49< 

3070 

?75868665090lo(> 

SIMPLE  DiriSIOK. 

i    -i   "o  !h   to  lind  how    often  one  number    h   contained 
:u.i.ii)Lii<'r  ot  the  same  luime. 

The  number  Given  to  be  divided,  is  called  the  dhideal 
Tlie  numbei  bv  which  to  divide,  is  talked  the  dhisv> 


MMPLE    DIVISION.  17 

live  numboT  of  tiiucs  tlic  dkhor  is  coiit;iined  in  tbo  cli-lh  nJ 

called  the  quotient. 

The  remainder,  if  there  be  iiny,  will  be  less  than  thv;  u'.tto'^,. . 

PuooF. 

Multiply  tlic  quotient  by  the  divisor  ;  to  the  product  add 
tiie  remainder,  and  the  bum  will  be  equal  to  the  dividend,  i' 
the  work  be  right. 

Examples,  V 

»-    Dividend'. 
Divisor      i;?)6<)45  68946*  3)27<3S954:- 


Quotrcnt       3472SU73  9229S4861  Vl ' 


Proof  6c}4j68946"  .      276S9j-] 


Dividend.  Quotient". 
Divisor     52)645;o436(124912 
52  52 


129 

104 

249824 
624360 

12  Kern; 

^'^A 

*208 

6495436  Prooi 

474 

468 

t)3 

b'2 

12 

2  2' 

.^4 


IS 


SIMPLE  DIVISION. 


Quotient. 

Rem. 

4  : 

Divide  8965462 

by  6   Ans 

;.  1494243 

and  4 

5 

3728675 

8 

466084 

3 

6 

4054682 

9 

517 186 

8 

7 

2768967 

10 

^276896 

7 

8 

19^9952 

11 

17726s 

4 

9 

2968967 

12 

247413 

11 

10 

5268794- 

20 

263439 

14 

11 

29619145 

40 

740478 

25 

12 

419825367 

5G0 

839650 

367 

13 

296876234 

64 

4638691 

10 

14 

47989536925 

735 

65201886 

,715 

15 

26574983184 

8962 

2965Q96 

432 

16 

53479689236 

7684 

6959S7G 

2052 

17 

491796S967 

"^SMJ 

2084768 

1255 

IS 

325S675689 

67^35 

48323 

14184 

When  the  divisor  is  a  compound  number,  that  is,  if  any  two  figures,  being^ 

ukiplit'd  together,  wiii  m.al\e  tliat  number,  then  divide  the  dividend  by  one 

;'  figureb,  and  tJie  first  quotient  by  the  other  figure,  and  it  will  then  give 

ticnt  required. — But  as  it  sometimes  happens  that  there  is  a  remainder 

c.-.ch  of  the  quotients,  and  neither  of  them  the  true  one,  it  may  be  found  bj. 

.is 

Rule.     Multiply  the  first  divisor  by  the  last  remainder,  and 
the  product  add  the  first  remainder^ which  will  give  the  trtie 


Examples, 

BJvide     296876234     by     64 
8)296576234 


•  8)37109529—2 


Quotient 


•  divide     875763S  by  28 
Quotient  312772  and  19rem. 
Divide        1571196  by  72 
'J;autient      ■  21822  and  12  rcin^ 


4638691  aiid  1  X  84-2  =  10  remaining. 
Divide     18957492  by  42 

451368  and  06  rem. 


Divide  3751749  bv  96 


39080aud60reiT:. 


MONEY,  NVEIGflTS^MEASURES,  ^c.  15 

MISCELLANEOUS  QUESTIONS. 

1.  Add  5621G3,  219^)4,  56321,  18536,  4340,  279,  and 
S3  together.  Ans.  6Y)36'86. 

2.  What  number  is  it,  which  being  added  to  9709  will 
make  110901  ?  Ans.   101 192. 

3.  General  \yASiiiNGTON  was  born  in  the  year  1732  ; 
liow  old  was  he  in  1799  ^  A^^s.  t^J  years. 

4.  Add  up  twice  397,  three  times  79^,  four  times  3176^ 
five  times  15880,  six  times  95280,  and  once  333040. 

Ans.  One  Million. 

5.  A  cashier  received^  viz.  Four  hundred  and  nine  dollars^ 
Twenty  thousand  and  thirteen  dollars.  Eight  thousand  live  hun- 
dred and  ten  dollars.  Nine  hundred  and  twenty-eight  dollars  ; 
of  which  he  paid  away  Filteen  thousand  fifteen  hundred  and 
fifteen  dollars  :  What  was  the  whole  sum  he  received,  and  liov/ 
much  remains  after  deducting  the  payment  ? 

Ans.  He  received  298()0  dolls,  and  there  remains  13345  dolls^ 

6.  What  is  the  product  of  15927  multiplied  by  4009  ?. 

Ans.  6'3851343. 

7.  128  men  have  one  half  of  a  prize,  wortli  34560  dolliirs, 
to  be  equally  divided  between  them  :  What  is  each  man's  part  ? 

Ans.   135  dollars. 
Prove  this  answer  to  be  right. 

8.  Three  merchants.  A,  B,  and  C,  have  a  stock  ot  J4S76 
dollars,  of  which  A  put  in  4963  dolls.  B518S  dolls,  and  €  the 
remainder :  How  muih  did  C  put  in  ?         Ans.  4715  doikr&. .. 


TABLE  OF  MONEY,  WEIGHTS,  MEASURES,  4  c. 
Federal  Money. 

10  Mills ..make 1   Cent. 

10  Cents 1   Dime, 

10  Dimes,  or  100  Ceiits • '1  J 

10  Dollars. ..i   1_^_ 

Ex G LIS II  Money. 

4  I'arthings make.  •  • • .  1   Fenny. 

ji  2.  Pence 1  Shillinc, 

'^0  Shillings  r.»^,»  ,,tf  •»•»»•».  .^«».«   I  IVuudf 


iO  MONEY,  \VL:iGnTS,  ^MEASUilCS,  ac 

rEi.'Cii  Tahi.e.  Shillings  TAnir, 

d.                  s.    d.  s.                     £,    6\ 

20 are- .1     8  20. .  • -are. . .  •!     0 

30 2     6  SO 110 

40 3     4  40    .   -* 2     0 

50 4     ^  50 2  10' 

60 5     0  60 5     0 

70 5  10  70 3  10 

80 6     8  80 c 4     0 

?0 7     6  90 4  10 

100 8     4  100 5     Q 

110    9     2  110 5  10 

120 10     0  .         120 6     0 

130    10  10  130 6  10 

140 11     8  140 7     0 

150 12     6  150- 7  10 

200 16     a  200 10     0' 

Troy  Weight. 

i24  Grains make •  •  •  •  •  1  Pennyweight,. 

QO  Pennyweights  •  • *  •  •   1  Ounce. 

12  Ounces.  ..•.»..........* 1  Pound. 

Xori:.     By  this  weight  are  weighed  jewels,  gold,  silver  and  liq\iors. 

Avoirdupois  Weight. 

1 6  Drams make  •  •  • 1  Ounce. 

1  ()  Ounces  •  •  •  • 1  Pound. 

28  Pounds » 1  Quarter.. 

4  Quarters  ....*.... 1  Hundred  weight.. 

20  Hundred  weight I  Ton. 

Noi'K.  By  this  weighs  arc  weighed  such  commodities  as  are  coarse  ancf 
ii'.lycct  to  wasle,  and  all  metals,  except  gold  and  silver.  One  pound  Avoir- 
iu^joij  is  equal  to  14  oz.  1 1  p  vt.  and  I5f  grs.  Tio;y. 

Apothecaries   Weight. 

20  G  rains  •  • •  •  •  •  make  -  •  •    • 1  Seruple.- 

3  Scruples •  ...••,  .  * l  Drain, 

8  Drams*  .•...  •• i  Ounce. 

1 2  Otmces 1  Pound. 

Kots.  Apothecaries  use  this  weigh'  in  coinpoimding  their  medicine^  j  K^t 
t^cy  buj  and  sell  their  drugs  by  Avoirdupois  weight. 

Cloth   Measure. 
4  Nails  -  • make •  1  Quarter. 

4  Quarters » -  •  •  •  —    1  Yard. 

?  Quaiters 1  Kll  l-ieiyii^^\. 

5  Quarters 1  Kll  Kn-li.vh 

tj  Qua: ;.  io  ..  c  r  ..... » 1  Lil  Prciicii. 


.MONEY,  WEIGHTS,  MEASURES,  &c.  2t 

Long  Measure. 

3  Bailey  Con>s make ••••••!  Inclu 

12  Inches •.... I  Yoot, 

3  Feet 1  Yard. 

5^  Yards,  or  l6\J  Feet 1  Pole,  Rod,  or  Perclu 

40  Poles • •  •  •  •  1  Furlong.. 

8  Furloiigs - 1  INiiie. 

3  Miles • • 1  League. 

()0  Geographical,  or  7  ,  ^ 

6yi  Statute  MUes     J    1  Degree. 

Note.     Li  this  measure,  le-ngth  only  i&  cuiisiJcrcd. 

Land  oit  Square  Measuhe. 

144  Square  Inches  •  •  •  •  make  •  •  •  •  1  Square  Foot. 

9  Feet 1  Yard. 

30i  Yards,  or  7  -,  r»  7     n    i        t>      v 

.->-ni  T-    ^  c    1  Pole.  Rody  or  Perch, 

2/24  reet  j  ^         ^ 

40  Poles  or  Perches 1  Rood. 

4  Roods 1  Acre. 

Note.     This  measure  respects  length  and  breadth* 

Wine  Measure. 

2  Pints make 1  Quart. 

4  Quarts  • ••• *  1  Gallon. 

42  Gallons 1  Tierce. 

()3  Gallons •  • • 1  Hogshead. 

84  Gallons 1  Puncheon. 

2  Hogsheads 1  Pip#  or  Butfe, 

2  l^lpes  or  4  Hogsheads  ••••••  1  Tun, 

Kon:.     I'he  wine  gallon  contains  231  cubic  inches.  j 


I 

11S^^« 


LE  AND  Beer  Measure, 

2  Pints •  --^  •  •  •  make •    •  •  •  1  Quart. 

4  Quar^«Bt*-«  • » 1  Gallon. 

8  CiiillonsW. .  • 1  Firkin  of  Alo. 

"  ^  ■    Ions  •  •  • • 1  Firkin  of  Bet.  r. 

ins  •  •  • • ••....  1  Kilderkin. 

'^  iviuierkins  •••••• •....!  Barrel 

■>4  Ihillons 1  Hhd.  of  Beer. 

3  Barrels  . . . .  f^. •  •  •  1  Butt. 

Noir.     The^le  gallon  contaiiis  ^82  cubic  inches, 


22  MONEY,  WEIGHTS,  ^MEASURES,  &c. 

Cubic  ok  Solid  Measure. 

1728  Inches make 1  Foot. 

^V  Ecct V 1  Yard. 

40  Eoet  of  round  Timber  or  7  _  „,  .       , 

50  Feet  of  hewn  Trml>cr         \     1  1  on  or  LoacL 

l!28  Solid  Feet 1  Cord  of  Wood. 

KoTE.  8  feet  in  length,  i  in  breadth,  and  4  in  height,  making  128  solid  ket,. 
contain  a  cord  of  wood.     Ihis  measure  respects  Icuglh,  breadth  and  thicknc&s. 

Dry    Measure, 

^  Pints make 1  Quart. 

i2  Quarts  •  •  • • •  • 1  Pottle.. 

'2  Pottles ' 1  Gallon. 

^    i2  Gallons 1  Peck. 

*  Pecks 1  Bushel. 

^  Bushels  .  • • .  1  Strike. 

4  Bushels 1  Coom. 

8  Bushels 1  Quarter. 

36'  Bushels 1  Chaldron. 

5  QjLiarters •  • •'  i% .   1  Wey. 

tl  Weys ; •"■-  1  Last. 

Note.    The  gallon  dry  measure  contains  268  J  cubic  inches. 


Time. 

f)0  Seconds make •  •  •  1  Minute* 

(}0  Minutes* .....................  i  Hour. 

24  Hours    1  Day. 

3(v5  Days 1  Vcar. 

NoTF.     S65  chys -^  hours  48  minutes  57  seconds  make  a  solar  }ear,  ac- 
cording to  the  uwst  exact  observation. 

The  iJdmher  of  days  in  oaek  month  is  thus  found  : 

Thirty  dai/s  hath  September ^  Jpi'ily  JunCy  and  Norcwher ; 
ycbniarii  hath  twenty-eight  aloney  and  all  the  red  have  ihirty-one. 

When  the  year  can  be  divided  by  4  without  a  remainder,  it 
£bssextiJc  or  Leep-Ycav,  in  which  February  hath  2'9  days. 


COMPOUND  ADDITION,  US 

COMPOUND    ADDITION 

Teacheth  to  collect  numbers  of  different  dcRominations  into 
ne  total. 


Federal 

M( 

i}NF>Y. 

D. 

C. 

M. 

D. 

C. 

M, 

i74 

74 

3 

396 

J4 

4 

198 

^9 

3 

147 

19 

5 

157 

1^ 

4 

149 

57 

9 

1^6' 

7(i 

9 

157 

83 

8 

English  Money. 


£. 

^. 

d. 

149 

14 

6-4 

387 

19 

8-^ 

*2.'>9 

1() 

7i 

874 

17 

4* 

678 

15 

(^^2 

Trc 

Ih. 

oz. 

dui. 

5''*- 

48 

7 

14 

19 

9.> 

4 

17 

'22 

i27 

5 

14 

15 

6ly 

6' 

19 

1() 

Id 

7 

13 

15 

£. 

^. 

d. 

If  14 
'^376 

\6 
18 

6h 

8| 

14 

9.'> 

2^6' 

16' 

7-^ 

174 

17 

10^ 

Troy  Weight, 


lb. 

oz. 

dxLt. 

^'•^ 

83 

11 

15 

O'.? 

15 

6 

16 

i:v 

21 

8 

19 

'^."'> 

33 

9 

15 

14 

46 

4 

13 

-  17 

Avoirdupois  Weight. 


\)n. 

CrtY. 

^r. 

lb. 

t>z. 

dr. 

Cxif, 

qr. 

!h. 

18 

17 

1 

14 

13 

13 

59s 

1 

^9 

36 

15 

3 

16 

13 

15 

187 

3 

19 

-:) 

15 

2 

19 

12 

13 

159 

2 

25 

1-V 

16 

3 

27 

14 

12 

283 

3 

1  > 

K) 

•19 

0 

25 

13 

10 

146 

0 

IS 

57 

17 

1 

14 

15 

9 

259 

1 

22 

24  CO^rrOL^ND  ADDITION, 

Apothecaries'  Weight. 


Ih, 

oz. 

dr. 

sc. 

5:^- 

lb. 

0^. 

(/r. 

,  ^r. 

.C^. 

3 

7 

5 

1 

17 

o 

5 

3 

2 

1! 

1 

3 

o 

2 

13 

1 

2 

2 

1 

14 

2 

5 

3 

o 

U 

3 

3 

5 

o 

13 

3 

4 

2 

1 

15 

5 

5 

4 

1 

12 

5 

o 

2 

2 

17 

2 

9 

3 

o 

15 

2 

3 

1 

2 

18 

1 

6' 

4 

2 

17 

Clcth  Measure. 
5/^.    q7\  Til,         E.FL  qr,  nl,         E,Ir,  qr,  nh        E,E,  qr,  nf. 


571 

1  3 

873  2 

3 

i81  2 

2 

56     1 

2 

184 

2  2 

396'  2 

2 

19<3  3 

3 

li)  2 

3 

190" 

2  3 

158  1 

1 

157  4 

0 

14  3 

2 

283 

3  2 

147  2 

3 

168  3 

3 

26*  4 

3 

u6* 

2  3 

326  2 

2 

193  5 

2 

S3  2 

2 

375 

3  2 

XP4  2 

1 

214  2 

3 

57     3 

3 

Win 

■E  M: 

EASURE.  • 

~ 

.Vv.;*.*'-- 

Tz/;?.  ///zc/, 

,  gal  qt.  pt. 

TurJM, 

^^^-  5^^!iiil^ 

187  1 

17  3   1 

176 

3 

16 

2*^  T 

56*  3 

15  2   1 

59 

2 

57 

3   I 

<)  1 

29  3   1 

S 

3 

14 

2  1 

36'  2 

18  2  1 

17 

2 

19 

1  1 

217  3 

57      1   1 

16'8 

1 

38 

2   1 

56     1 

46  2   1 

25 

2 

52 

3  i 

Ale  and  Beer  Measure. 
hhd,  gaL  qt.  pf.  hhd.  gaL   qt,  pt. 


49 

38 

2 

78 

17 

3 

38 

45 

^ 

_  • 

39 

16 

0 

57 

48 

2 

15 

51 

3 

49 

37 

1 

76 

43 

2 

57 

26 

2 

23 

26* 

3 

28 

18 

3 

52 

33 

2 

_.— , 

COMPOUND  ADDITION. 


^r. 

Oi(S/i. 

yjcA-. 

qt. 

57 

4 

<) 

1 

19 

5 

3 

1 

3S 

() 

o 

»> 

'.7 

7 

3 

7 

o 

3 

1 

4 

9 

o 

o 

o 

72 

5 

c 

Dry   JNlEAsuin-.. 

iihaJ.  hush,  pcic,  nf, 
57  ()      31      1       ■ 

y}       ()     1     G 
U      1.3      2      S 

32      eO      3      '.! 


Long  IMeasuuk. 


t/i'.^. 

7viL 

Un\ 

po. 

ft. 

//?. 

bar. 

wil. 

/.r. 

;;.9. 

7/f/.  ft. 

217 

17 

7 

19 

14 

9 

1 

87() 

7 

13 

4  2 

/  33 

17 

4 

id 

13 

3 

2 

129 

6* 

2() 

2   1 

283 

53 

5 

19 

12 

2 

o 

l()7 

4 

5  9 

3  2 

346* 

20' 

6* 

23 

13 

4 

1 

157 

3 

l':^ 

<;   2 

189 

32 

3 

27 

14 

5 

o 

28() 

2 

2? 

1  •^ 

17  () 

14 

2 

15 

15 

6 

«-■) 

191- 

^) 

•V") 

o   *<  > 

921 

15 

4 

18 

IG 

7 

I 

17  (; 

4 

18 

5   2 

Land  IMeasure. 


(icr. 

ro'). 

7;n\ 

(lev. 

TOO. 

T^fr. 

7-n 

1 

19 

870 

3 

19 

6"9 

3 

29 

19 

o 

16' 

]5 

2 

16' 

54 

3 

S7 

37 

3 

14 

129 

o 

26' 

16- 

2 

13 

187 

3 

14 

29 

3 

27 

i:;(; 

<> 

1!) 

Time. 
f/r.9.  J(7//s\  //r.y.  2;?/^?,  sec.  vrs,    iJa'/s.  /ws.  nn,i.  5* .  , 

i87      149      14      13      )2 


14(> 

126 

16 

16 

16 

.39: 

180' 

19 

'^9 

lf> 

;e8 

140 

21 

46 

35 

•? 

119 

22 

IS 

26 

146'  . 

146 

19 

57 

19 

. 

3f)0 

1 6() 

14 

16 

n 

19 

186 

17 

16 

16 

4  6 

147 

15 

^9 

19 

87 

196' 

23 

46 

4-7 

157 

219 

14 

.'2:^ 

16 

46 

138 

15 

42 

1 ,3 

2o  co:\irouND  subtraction. 

CGJIPOUXD   S  UBTRACTION 

Tcndictb  to  find    the  invcjuahty  between  niiinbcrs  of  divers 

tleiioniinaljuiis. 

Federal  JMoxev. 


doL     ct. 

w. 

f?0/. 

ct. 

m. 

^/(v/. 

ct.     m. 

''■!-     5;5 

i 

433 

CO 

1 

17  0 

30     3 

■     !/7 

o 

.9 

1.5 

5) 

[) 

50     2 

]■  roni    1 0  1      1  I 


'lake    lU      1()      21 


Ex  G  LIS  II    iMoXLY. 

.       d.  ,.     ^-C.      ^.       f/. 

304     19    «i 


From  389      18     0| 


'I'di 


19     4 


100        0 
11      11 


TncY   Weight. 
IA.     or.   did.  gr.  I!k     oz.  dirt,   gr. 


From   87      H      11      K 
Tcl.e    19      11      14      22 


27      10      15      2'2 
15       9      16"     23 


AvoiuDurois  Weight. 

ton.  cut,  qr.  lb.  oz.  dr. 
From  100  10  1  11  11-  13 
^^ake      15      13      1      18      12      15 


cut.  qr.  Ih. 
59  1  1 1 
19     3     27 


AroTHECArviEs'  Weight. 
Ih.  oz.  dr.   sc.    rry,  //).   OZ.  dr.  sc.  gr. 


!    Ill      2 

ikc    1 

3 

7 

4 
5 

1 

o 

J  3 
10 

2 

1 

1 

4 

3 
o 

1 

o 

15 

17 

_, . 

.. 

COMPOUND  SUIVrilACTlON. 
Cloth   ^^Ieasiih:. 


yd. 
From  ^251 
Take   1::/ 

qr. 
1 
:3 

?.'/. 
3 

1-0     ^     \> 

-11:)     ^     '• 
1 '{ -t     .J     '^ 

w.  ,  ,  . 

tun,  • 

'"•/■'• 

800      . 

'J      i 

149     2 

61 

3      I 

^«;7.  7///^.  g^/.  qt,  pt. 
From  591  1  13  1  1 
Take   VlG     i2     56'     3     1 


Ale  and  Beer  ]Measur:-. 
hd,     gal.    gt.pt.  '     /id. 

From  571      19     3      1  lOO     ^b     '2      1 

Take  198     53     2     1  9     C7     3      I 


Dry  jNIeasukk. 

qf\  hu,  gal.  qf,  c/iul.  ha.  gaL  qt. 

From  38     4     5     3  6'9     21  "  3   ^2 

Take   17     5      1     2  49     S3     5     '^ 


Long   ^Jeasure. 

jft 

d(g.     m.  fur.    p.    f.     ill.  b, 
j-^orn  8 19     13      1      19      1 1     3      1 
'lake   159     4-9      2      27      10      8      2 

♦ 

2< 

^-  fn:               : 

19     :'^               I 
59     7      l.>      12 

— 

- 

Land   IMeasure. 

acr.  ro').  J  r)-.                acr.rco.pcr. 
From  5CU      l     'u                r,Ol      3      13 
'lake    l':9     3      15                1<  0     2      21 

acr.  )00.  pry, 
21'-      '^   '  ■;  1 
1 .. 

. 

■ 

'i'll'.IE. 

?//>.      da.     hr.      w.   Acr,  urs.  da.  /'/.  //'. 

l^;om    I7i      143      11      ]4-      19  is  i  I  111  1.)  CJ 

'lake    12s      1/i-      \[)     51      1  i  3^.<)  1<;0  21  -1  o 


C8  PRACTICAL  Ql;ES•['K)N^. 

PRACTIC.il  questions  ly  COMPOUNiy  addi. 
TION  AND  SUBTRACTION. 

1.  Cast  up  tlie  followino- sums,  viz.  twenty-tliree  sliilling^ 
-■  ■!  !'vo  prnco,  one  pound  ancl  nino  pen.co,  se\'en  shillings  aiut 
':^--..i  jrnco  three  larthings,  twenty  pounds  thirteen  shtilin^s 
'i.'.J,  nii.o  pence,  lifteen  pence  three  farthing-^. 


£. 

s. 

cL 

1 

3 

5 

1 

0 

9 

0 

7 

H^ 

QO 

1:3 

.9 

0 

1 

3* 

7        24 

Pi'ool'  ^'.  <^3         7         2i 

2.  Tvvcnty  dollars  and  four  cents,  five  c?onars  and  thre« 
JDilis,  eighty-two  cents,  fcix  dollars  and  five  mills. 

Ans.  31  dols.  8()  cts.  8  m, 

3.  Seventy  dollars,  tlirec  dollars  and  three  cents,  thirty^ 
four  cents  and  four  mills,  eighty  dollars  and  a  half,  six  dollar* 
1  r.,;  a  (pciarter.  Am,   lO'O  dols.  r2cts,  4  mills. 

'i'en  pounds  and   threepence,    forty-five  shillings  and 

''"■'-  half  penny,    thirty-seven  shiljings   and   four-penc« 

liings,    nine  pounds   and  three  fart'hings,   one  shilling 

411. 1  M.\  pence  farthing,    eighty- two  shillings  and   four-pence 

^.ali-penny.  Ans.  £.27  7  5|. 

5.     Thirty  dollars  six  cents  and  a  half,  fifty-three  cents  and 
hue  quarters,  eleNcn  cents  and  a  quarter,  nine  dollars  eleven 
coi2ts  and  a  half,  fifty-four  cents.  Ans.  40  dols.  37  cts. 

(j.  Take  three  shillings  and  four  pence  from  one  pound  tw© 
j^Jjidings  and  a  penny.  Ans.    ISs.  gc/. 

7.  From  c€.5  2.;?.  Id.  take  nine  shillings  and  six-pence  half 
poM;y.  Ans.  £A   12  6*|. 

[•'."^    Take  twenty  shillings  and  three  forthinjis  from  £,S, 

Ans.  k\  6'  \9  111, 
,     ').     From  IS  dollars  take  eight  mills. 

Ans.    ]7  dols.  99  cts.  2  n  . 

10.  Take  53  dimes  from  53  eagles. 

Ans.   524-  dols.  7  dimes  or  70  ct^. 

11.  A  merchant  bought  112  bars  of  iron,  weiiihii^o  n()c\\{. 
1  qr.  1 1  lb.  of  which  he  sold  59  bars,   weighing  2|;  c  , 


RCDUCTIOX.  '."^i 

!?r  ffr.  ,~  how  many  bars  has  he  remaining,   and   what   is   ia,: 
wc'i^lit  ?  Ans.  53  bars,  weighing  26  cwt.  1  qr.  18  lb. 

12.  Required  the  total  weight  of  4  hogsheads  of  sugar, 
weighing  as.  follows,  viz.  No.  1.  p  cwt.  2  qrs.  21  lb.  No.  2. 
10  cwt.  5  qrs.  23  lb.  No.  3.  8  cwt.  2  qrs.  ?5  lb.  No.  4.  9  cwt. 
3  qrs.  17  lb.  '  Ans.  39-Cwt.  1  qr.  2  lb. 

13.  A  ropemaker  received  3  tons  15  cwt.  3  qrs.  14-  lb.  of 
hemp  to  be  wrought,  of  which  he  delivered  in  cordage  34  cwt. 
1  qr.  22  lb.  ;  how  much  remains  ? 

Ans.  2  tons  1  cwt.  1  qr.  20  lb.. 

14.1^  Received  57953  niills,.  4953  cents,  1913  dimes,  and  45» 
eagles  ;  required  the  total  sum  ? 

"    •  Ans..  748  dols.  78  cts.  3  mills. 

J  5.     A  cashier  received,  viz.  one  hundred  pounds  and  nine- 

nee  half-pennv,  three  thousand  seven  hundred  and  four 
*>uunds  ten  shillings,,  twenty  thousand  and  ninety  pounds  two- 
sliillings  and  eleven  pence  three  farthings,  of  which  he  paid 
away  sixteen  thousand  sixteen  hundred  and  sixteen  pounds  ; 
how  raucli  has  he  on  hand  ^  Aiis.  <£.()278   13  9,^. 

1().  A  farmer  bought  three  pieces  of  land^  measuring,  viz^ 
riie  lirst  piece  21  acres  3  roods  19  poles  ;  the  second,  37  acres 
2  roods  29  poles  ;  the  third,  27  acres  2  roods  25  poles  ;  of 
which  he  sells  15  acres  2  roods  39  poles  ;.  how  much  has,  he 
remaining  .?  Ans..     71  acres  1  rood  34  poles. 

17.  A- has  paid  B  £.9  15  6^,  £A9  11  5l|,  .€.14  I9.7hr 
and  54>9.  S^d.  on  account  of  a  debt  of  .€.50;  how  much  ij* 
llu-ie  still  unpaid  ?  Ans.  €.2   18   9^. 


REDUCTION-^ 

Reduction  teacheth  to  change  numbers  from,  one  dettcHtl^ 
nj.tion  to  another,  without  losing  their  value. 

liUL£.  \Vhen.  the  lleduclion  is  descendijii^,  multijdy  tiie- 
higliO-.t  denomination  by  as  many  Qf  the  next  less  as  inake  one- 
<>f  '.be  greftter,   lulding  to   the   product  tlic  j^arts  of  t-h<^  sanie 

:;e;  u^id  SO  on  to  tiie  last. 

'•'vhen  the  Reduction  is  ascending.,   divide   the  give?i.  mim^ber 

ajy  rAa-ny  of  tfuit  denominatioa  as   irudsc   oue  of  the   no"?^K 

LhqVr  and  so  on  to  the  denominatioa  required^  and  thtt  h»-"t: 
tient    with,    the  .-  laiuder^    (it   aii^)    w-iil  l^  \Lii: 

-..^wer- 

S^bm  yrouf  isj.-y  revor^ing  the  qti^btioa*. 


)  REDUCTION. 

FeI>E11AL    iNIONEY. 

I,     In  53  dollars  how  many  mills  ? 
63  dolls. 

10  )       Or  decimally,  by  adding  a   cypher 

for  each  inferior  deuomination,  ihus, 


530  dimes. 
10 


5300  cents. 
10 


(lol.d.cjii. 

Ans.    53000  mills.  53,000 

'2.     In  14000  mills  how  many  dollars  ? 
10)14000 


yOr  decimally,  by  s^^paratincj  the  f]i^nre?> 
10)1400<       coiin;ini^  from  the  riglit  to  the  nam® 

J      rec^aired,  thus, 

10)  140  (^ 

doJ.d.c.m, 

Alls.    14  dolls.  14,000 

J.     in  57i}35  mills  how  many  dollars? 

Ans.   57  dollars,  93  ce-nts,  and  5  mills-. 

4.  How  many  eagles  in  1933  dimes  ? 

Ans.   19  eagles,  3  dollars,  3  dimes.. 

5.  In  1290  mills  how  many  dimes  ? 

Ans.    12  dimes  and  9  cents. 
^.     How  many  cents  in  45  dollars  ?  Ans.  4(i00. 

7.     In  19OCO4  mills  how  many  doilars  ? 

A\\<,    190  dollars  and  4  mills.. 

E  X  G  L 1 S II     ViO  X  io  Y . 

\.     Ill  £jn      1  y      3h  how  manv  farthings  ? 

Proof.. 


'20 

11 

3 

^ 

1; 

>31 
i  J 

shiil 

ing^ 

•- 

1?  ■ ' 

4 

pen< 

"C, 

4;  ^7 


en  > 


!:o )  10.31 - 


.r^i  11  :^' 


Ans.     8/ 902  farthings. 

'J.     How  many  povmcis  hi  3175  larlhing.^  ;     Au>:, 


REDUCTION".  31 

3.  In  l[).s.  S|r/.  how  man}^  f«rthings  ?     Ans.  ()\7  fluthings. 

4.  .  How  many  pouiuis  in  i)7o2  pence  ?       Ans.  £A0  12   S 

5.  In  £a6  lio'.v  many  crowns  oi  6s,  JcL  each  ? 

x\ns.    13.9  crowns  and  4-  shillings  and  1 1  pence. 
6\      Mow  many  pounds  in  493  dolLiis  ?  Ans.  £AA7    l.S 

7.  In  14-3  pence,  ' •  r—iy  shillings  ?  Ans.    ils.    lid. 

8.  Reduce  3S.V.    1  ii'pciije.       Ans.  i)2 1  half  pence* 
Prove  tlic  above  ii!isv.c'i.^  lo  be  right. 

TiioY    Weight. 

1.  In  151b.  troy  how  many  grains  ?  Ar.s.  S()400  gr;?. 

2.  How  many  ounces  in  ^749  dwt.  ?     Ans.  287  oz.  9  ti'"^^' 

3.  In  1 1  oz.  13  dwt,  13  grs.  how  many  grains  ? 

An«.   oCOj  p;r-^. 

•     4.     IIow  many  grains  in  15  spoons,   cac'i  !g  6  dwt. 

15  grs.  I  ■       ^'385  grs. 

Avoirdupois  V/eigiit. 

1.     In  19  tons  14cwt.  2  i\v<,  19  lb.  lie  :• 

ny  d  rams  f  Au>.    i  i.ji  v  i.j/  . ; ,  5 . 

"^  2.     How  msny  cwt.  in  ^5^63  lb.  ? 

Ans.   S5  cwt.  1  ([Y.  15  lb., 

3.  In  13  cwt.  3  qrs.  21  ib.  how  many  pounds  ? 

Ans.    156i:lb 

4.  How  mnr.y  mc^s-pieccs  of  4;Ub.    and  3h  lb.   of  each  ai. 
equal  nuniLc!,  va  3  I  cwt.  1  (jr.  12ib.  of  beef  ? 

Ans.  439  pieces  of  each* 

Wine   ^Ieasure. 

1.  In  25  tuns  of  wine  how  many  pint-.  ?     An.s.  50400  pints. 

2.  How  many  hogsheads  in  4935  ([uurls  ? 

An?.    19h.  3()g.  3f[t. 

3.  In  3  hlids.  13  gals.  2  qts.  Uow  many  half  piutb  ? 

Ans.  3240  half  pints.. 

CtOTu   Measue?., 

vards  how  manv  nails  ?  Ans.   252S  nailn 

2.      iiow  niany  ells  Engii 


•..  5 


Ans.  C9(i'-'l!s  3  q;- 
'-'9  pieces  of  .h.ollandj  each  containing  3()  eiN  Th'}:, 
-   -—  ■-•  -  ?  An-,   "  ^  '  ■■  •' 


52  nEDUCTior^. 

LoxG  oMkasure. 

1.  In  29  miles  how  many  inches  ?      Ans.   lS3r-i4<0  rnciiea*. 

2.  How  many  furlongs  in  19753  yards  ? 

Ans.   89  fur.  173  yds,, 

3.  h\  590057  inches  how  many  leagues.  ? 

Ans.   3  leag.  2  fur.  110  yds.  If.  5  in. 

Time. 

1.  How  many  hours  in  57  years,  allowing  each  year  to  be 
"6j  days  6*  hours  ?  Ans.  499662  hours. 

2.  In  57953  hours  how  many  weeks  } 

Ans.  344  w.  6  da.  17  hr. 

3.  IIov>  -ys  from  J 9th  of   INlarch    to  the  23d  Sep- 
tember toM  Ans.   188  days. 

4.  How  >   lys  fiom    24th  May,   1797,   to  15th  De- 
cember, 179'^  ^  Ans.  570  daysv 

Land  Measure. 

7.     In,  41  acres  2  roods  14  perches,  how  many  rods  ? 

Ans..  6654  rods  or  perches., 

2.  How  many  square  rods  in  7752  square  feet  ? 

Ans.  28  rods  129  f^et.. 
3..    In  5972  perches^  how  many  acres  ? 

Ans.  37  ac  1  rood  12  per^ 

Solid    Measure^ 

1       Til  -1  i^i^e  of  wood   96  feet  long^,,  5  feet  high,   anri  4  fcot 
\^ ;  .-:;:ny  cords  ?  Ans.    15  Coi'ds. 

...  .,2  toiis  of  round  timber  kow  ma,ny  inches  ? 

Ans.   56'()7840  inches. 

3.  \^'!!nt  r.ri^  tn?  contents  of  a  load  of  wood,  6  i'eet  hjng,  4' 
i.Vi  h:L':u  iiLu  J'  i\vt  wide  ?  Ans.   3j  leet. 

.I'S    are  y.o]<]   by   the  cubic   foot,,  co! 
■    '   ''  ;^  cu]ii.(  iils  c.;e  ihi's  found  ; 

'  ■•-  .■;--!. u:-  add   half  of   rh-  rr:.^:-,.h.,- 
y-  rhc  same  half,    . 

v'ubic  foot,    -dnd    liic    quu'.iout    is   the 
uv  ,ii.ed^ 


REDUCTION.  3a 

Examples. 

4.  I  low  many  cubic  feet  in  a  grindstone,    24?  inches  diam- 
eter, and  •!•  inches  thick  ? 

24  diameter. 

12  half  diameter. 

36 
12 

432 

4  tliickuess* 

172H)J72S 
Alls.     1  foot. 

5.  What  are  the  contents  of  a  grindstone,  36  inches  cHam^ 
etcr,  and  4  inches  tliick  ? 

36 
18 

54 
18 

54 

972 
4 

1728)3888(2^ 
3456 

432 
4 


1728)1728(1 
1728 


Ans.  2l  cubic  feet* 


3i  REDUCTION. 

AMEIUCAX  MONIES. 

To  change  New-England   nud  Mrginia  currency  to  Federal 
niunev,  the  dollar  bein^  !>  -^^'im.^^. 

lluLE.      As  llic  valu;  'iris  equal  to  three  tenths  of 

a  pi^und,  when  jxnuid^  i..v^.,wi  tu  be  changed,  annex  three 
cv}  iiers  lo  the  M,ni,  and  divide  the  whole  by  3;  the  quotient 
ib  the  answer  in  eents. 

Examples.      "* 
1.     Change  £.523  to  Federal  money. 
3)523000 


3  74333^^  cts.      Ans.   1743  dols.  33jctS 
Change  the  following  sums,  viz. 
£, 
5.     1 84  Ajis. 

3.  29 

4.  57     ' 

5.  219 

6.  81 

7.  127 
When  pounds  and  shillings  are  given,   to   the  pounds  annex 

half  the  number  of  shillings  and  two  C3'phers,  if  the  number  of 
shillings  in  the  given  sum  be  even  ;  but  if  the  number  be  odd, 
annex  half  the  number,  and  then  5  and  one  cypher,  and  divide 
by  3  ;   the  quotient  is  the  answer  in  cents» 

Examples. 

1.     Change  £.59  185.  to  Federal  money. 
3)59900 


dols. 

cfs. 

613 

33\ 

96 

66f 

190 

730 

270 

423 

33J 

19961);^  cts.      Ans.  199  dols.  66^  cts. 
Change  £.93   13.v.   to  Federal  money. 
3)936'50 

Ans.  312  dols.  I65  cts. 

dols.  cfs. 
Ans.  432  l6f 
212  50 
93 

609  83^ 
192  66i 
40t  50 


3121(51  cts, 

Chani^e 

the  following  sunis^  viz. 
£.     s. 

3. 

129   13 

4, 

63   15 

5. 

27    IS 

6. 

182    19 

7 , 

57-  16 

^-. 

121      7 

11  EDUCTION.  35 

Wlicn  Iborc  arc  slnllings,  pence,  c\'C.  in  tlio  given  ^nm,pr.n<'x 
for  the  shillings  us  befoir  directed,  and  to  these  add  the  lar- 
things  in  the  given  pence  and  ftirthinf:^.  observing  to  increase 
their  number  by  one  when  they  exv ;  i  1  J-  .uui  by  two  when 
lliey  exceed  37?  J^nd  divide  as  before. 

Ex>\MPL£S. 

1.  Chanizo  -^.Cl    Ss.  4jt'/.  to  Federal  money. 

i>)'Ji  I];j  4  is  aniicxed  to  the  p.ounds  for  half 

' the  shilbngs,    and    J 9    ft>i'  the    fiir- 

7  139!  ^"^s*        things  in  -ij^/.  and  excess  of  12. 

Ans.  71  dols.  :;;  ']  ci5, 

2.  Change  cf.  117   1^^-  ^<^^.  to  Federal  money. 

3)117808 

392(>9i  cts.     Ans.  392  dols.  69]  cts. 

3.  Change  .£.721   9s.   ll^r/.  to  Fet-leral  money. 

3)7214-97  In  this  example  4  is  awncxcd  to  the  pounds 

for  half  the  even  shillings,  and  47  for  the  far- 

240499  cts.       things  in  1 1^^^.  and  excess  of  37?  and  then  5  is 
added  to  the  figure  next  to  half  the  shillings, 
making  it  9  i'^^  place  of  4  for  the  odd  shilling, 

Ans.  2404  dols.  99  cts. 

4.  Change  £.29  1  Fv.  2^/.  to  Federal  men.-/. 

3;  29.^.^9 


Cii; 


9^^153  cts.   Ans.  9S  dols.  53  ct3. 


(Jols.   cts. 
'D   9  Ans.  8()  ()2;^ 


6".  24  11  7|-  81  94 

7.  1 238  10  94  4128  40' f 

8.  2001  1  31  6070  21 1 

9.  lo3  17  G  512  91J 


SG 


REDUCTION. 


A   TABLE 


lOR   CIlANGIlsG    SHILLINGS   AND   PEXCE  INTO   C£NT?5 
AND   MILLS. 


6/ 

liL 

d/i//^. 

^hiU. 

i7;ii/. 

ahUl. 

0 

1 

2 

3 

4. 

5 

pence.' 

cts. 

in. 

r/5. 

?•». 

cL«.  7n. 

rfs,  7?i, 

cts.  in. 

cts.  m. 

0 

16 

7 

33     3 

50     0 

66     7 

83     3 

1     ' 

1 

4 

13 

1 

34     7 

51     4 

68     1 

84     7 

1> 

2 

8 

19 

5 

36     1 

52     8 

69     5 

86     1 

•J 

4 

i> 

20 

9 

37     5 

54     2 

70     9 

87     5 

4 

5 

6 

2 '2 

3 

38     9 

55     0 

72     3 

88     9 

> 

7 

0 

2.  J 

7 

40     3 

57     0 

73     7 

90     3 

(5 

8 

:> 

1;'5 

0 

41     7 

58     3 

75     0 

91     7 

r 

y 

7 

£>-J 

4 

43     0 

59     7 

76     4 

93     0 

8 

11 

1 

^7 

8 

44     4 

61     1 

77     8 

94     4 

9 

i'i> 

5 

29 

2 

45     8 

62     5 

7  9     2 

95     8 

10 

1  ;^> 

9 

30 

6 

47     2 

63     9 

80     6 

97     2 

11 

1/> 

•■> 

32 

0 

48     6 

65     3 

82     0 

98     6 

To  cJiauge  Federal  Money  to  Ne^jc-Eii gland  and  Virginia 
Curreney, 

Rule.  When  tlic  sum  is  dollars  only,  multiply  it  by  3  and 
tlouble  th€  first  iigurc  oi"  the  proclucl  lor  shillings,  and  the  rest 
of  the  product  will  be  pounds. 

When  there  are  cents  in  the  given  sum,  multip''y  th.e  wliole 
Jjy  3,  and  cut  olF  three  figures  cf  the  product  to  the  right  hand 
tis  a  remainder, 

]Midti])ly  this  remainder  by  CO  and  cut  ofT  as  before. 

Proceed  in  this  manner  through  the  several  parts  of  a  pound, 
and  the  numbers  standing  on  the  left  hand,  make  the  answer, 
in  the  several  denominations. 

Note,  if  there  be  mills,  cut  off  fouriigurcs  and  [.roceed  as 
abo\'e. 

Example. 

1.     Change  872  dollars  to  New-England  txirrcncy. 
872 
3 

■  £,     ^. 

2(Jl    12  Ans.     2(U    \Z 


KEDUCTIOX. 


57 


12.  Civino;e  1971  dols.  96'^  cts.       3.  Reaace  1259  c^t^j"^.  ^"^.9  cts. 

lo  MabSiicluibClts  currency.  and  7  anils,  to  IMas^.  cnnvncy. 
1971  9^>!  '  ^ 

3  ^ 


(/.  9,6'0() 
4 


t\-.J 

r,9'^9t 

'^'0 

V        ] 

<?,;3S':0 

1'2 

f/. 

-1,5^40 

•i 

/:  2,400 


.^l-i  I 


/:  2,33&'0 
19  4i 


y/     r  .</  CLE 


7'br  chaiighig 

^Cenl 

.s  into  Shit  1 1 

ngfs^  Pence ^ 

and 

Ct'u^i'.  Cents. 

Cents. 

Cents. 

Centi.  1  Ccnc^.lCents. 

C('/.75.  Cents. 

'  10        20 

30 

^  40 

50  !     en  1    70 

80        ^> 

cents 

c/. 

S.        f/.!S.        f/ 

S.        (/. 

s.'   d. 

<. 

-.        (/.  s.    '  f/. 

0 

7-'.;l        '2- 

i        0} 

2.    4-1 

3 

t    L>^;5   4- 

1 

4 

8  it    :-;*■ 

L   10^ 

^    ^l 

3     (Hi  i     «  li     0 

4   10|o     5| 

2 

H 

i      ol 

1    11 

4     6\ 

5>li3     H 

4    3^ 

4  11    5     6i 

3 

n 

n 

I     4^- 

1  iH 

2     7" 

5     ^3     9i 

4     4-^ 

1  11|5     7 
.5     0|i5     7^: 
>     U^     8| 

4 
5 

3 

10 

10^ 

L     b\ 
1      6 

2    0| 
2     IV 

%     7-1 
2     81 

3     213  10 
3     3|t3  10-!- 

4     5^ 

4     (5 

6 

4 'J 

nPi    (>i 

2     2 

2     9 

3     4i.i      -^ 

)     2    5     9 

7 

5 

i    o|^:!     7^ 

2     l»t 

I     9-1 

3     5    4 

5     2|5     9| 

5     Sl\.^  lof 

8 

■H 

L      I'il      8' 

2    :>J: 

-i  10.^ 

3^  514     1     i     y 

9 

61 

1     l^il     81 

;i     4 

^  Hi 

3     6}  4     Jl4     8^ 

.5     4  !5   Ilk. 

'ncy 


fo  Federal 


To  cka.  :.~York  and  Novth-C. 

nwncijy  the  dollar  bi  ing  S  d/,ilLfigo.    , 

Rule.   Prepare  the  G^iven  buni  b^Mhe  rule  Tor  New-Kn '^'^'^cl 
Bioiiey,  and  divide  by  4  ;   the  quotient  is  the  answer  in  c.iilo, 

1.  Cliange  .£.4()1   to  Federal  money. 

4)451000*  ^ 


115:250  ct.^,      Ans.  1132  doli 


D 


e?  REDUCTION. 

'  ,;  n^c  cf.419   IQs.   S^d,  to  Federal  mcnry, 

104-883J  cts.     Ans.  1048  dolls.  So.^  ^'^' 

To  change   Tcdtral  ^aoncy   to  Neu-York   and  Norl/i-CaroIinn 
currcnciu 
KuLK,     As  for  MMSsacluiH'tts  currency,  Tising  4  as  a  iiuilti- 
plier  inbtead  of  3 ;  the  vidue  of  a  dollar  bciiig  Cvjuai  to  four- 
icnthb  of  a  pound. 

Example!^. 
1.     Change  l6S4  dollars  to  N^w-York  and  North-Carolina 
€urri-ncv, 

1684- 
4 

Ans.  £X)7o   12 
Q,     Change  1048  dolls.  S3f  cents  to  Nc^v-York  currency. 
1048, 83j 
4 


41 9,535 
'10 


8,400 

4 


1,GgO        Ans.  £.41.9   I0.s\   8] J. 

To  change  Ncxi-Jcrsey^    Peinisyhaiua,  Dclauare  and  Marylaml 
currency  to  Federal  money,  the  dollar  being  Js-  6rA 
Rule.     As  the  value  of  a  dullar  is  equal  to  g  o^  ^  pound, 
nivdtipiy  the  given  bum,   when  it  is  pounds  oidy,  by  8,  and  di- 
vide by  3  for  dollars,     U  there  be  shillings,  &c.  increabc  tlw 
§uni  in  pence  by  ^  of  the  whole  sum  for  cents. 
Examples. 
1.     Chan^je  £A7l  to  Fedjeral  money, 
471 
8 


3)376'8 


Ans.   l^aO^doliai-s. 


ItnDUCTION.  39 

ft     Cluvngc  .£.480   I.9.9.  (>/.  to  Federal  money . 

20 


KH^(ia|  cents,  Ai\^.  1':H'2  aoiln,  (;:j^  ct^, 

To' change  Ffdcral  monnj  foNew-Jerscij^Fennsj/hmuaj  Dilaxi\n't; 
and  MaryUmd  currency. 

RutP..  Multiply  the  sum,  when  fn  dollars,  by  3,  ami  divide 
by  8  for  pounds.  If  there  be  dollars  and  ccntj<,  multiply  the 
given  mm  by  90,  and  the  product  (rejecting  two  rigarcs  on  the 
right)  is  pence,  or  deducting  ^^  of  the  sum  •>iveb  the  pence  like- 
wise. 

Examples. 
1.    Change  125&  dollars  to  PennJ>ylvania  currencv. 
1255 
3 

S)37()iS 

Ans.  £a71 
,2.     Chan:z;e  \'2^2  dolls.  G3}>  cts.  to  Pennsylvania  cvirreu^^v., 
^'  128203.i  \)v  ,'o)12826'3.^ 


90 

12S26^^ 

3  2)11.5437,00 

12)115437 

20)9619—91 

20)9619— i> 

Ans.  cf .480   19  9  ^.480   \C)  9  as  before. 

To  c/aingc  Saiffh-Carolina  and  Georgia  a/rrcncu  to  Fediral  mo- 
ncii^  the  d/dliir  being  4a\  S(/. 

RuLF>.      As  tlie  value  of  a  dollar  is  equal  to  .■J^^  of  a  pound, 
.  ;!io  <i,ni  I  o  t^.uvirls  o!,b-,   multiply  it  by  T-O,   nivl  divide  by  J. 
for  (!  »!:  illin^>"s,  <S:c.  aiihiw  two  eyphrrs  to  the 

pen(  e  lii  i.jc  ^iM  I  ^^.ilI,   and  divide  by  .■)(),   liie  [h  iicc  iiv  a  dol- 
lar j  liie  ouotieiu  is  the  answer  m  eent^. 


40  REDUCTION. 

Examples. 
I.     Change  £,2S  to  Fctlcral  moiioy. 
28 
30 


7)SM) 

1'20  Ans.    1^0  dolU. 

2.     Cliapgc^.ll  4  8  to  Federal  money. 
11   4  8 
20 

224 
12 

^X7=:56  8)2()t}()'00 

7)33700 

4S14f  cts.     Ans.  48  dolls.  14 f  ct^ 
To  change  Federal  money  to  South-Carolina  4'  Georgia  current:}/. 
Rule.  Multiply  the  dollars  by  7,  and  divide  by  30  for  pounds. 
If  there  be  dollars  and  cents  multiply  by  36',  and  the  product 
(rejecting  two  figures  on  the  right)  iy  the  answer  in  pence. 

Ex  A  UV  LEU, 

1.  Change  540  dollars  to  S.Carolina  and  Georgia  currency,. 
540 

7 


3| 0)37^10 


AnL<.  £.120" 
2.     Change  48  ciolis.  14f-  cts.  to  South-Carolina  currency. 
4S14f  Ob 

db  2 


28884  7/H2 

24070 

l6  '                     ID 

12)':(\96",00 


20)2':4— 8 


11    4   8  Am.  £.11   4   8 


REDUCTION.  41 

"Jo  ..  ...^,-  Canada  (uui  Nova'Scoiia  currcuci/  to  Fcdcrahnonci/^ 
tt'ic  dollar  being  5  s/nllings, 

liULE.  As  the  value  of  a  dollar  is  eqiuil  to  one-fourth  of  a 
pourui,  multiply  the  suiiu  when  in  pounds,  by  4,  for  dolhirs. 

When  there  are  shiliini2;s,  <lkc.  redu-ce  the  given  sum  to  pence"; 
annex  two  cyphers,  and  divide  by  60,  for  cents. 

]\x  AMPLtS, 

1.  Change  £,S6  Canada,  currency  to  Federal  money* 

36 
4 

Ans.    1-44  doll^. 

2.  Change  £.528-  l2s,.Qd,  Canada  currency  to  Federal  money. 

20  Qr  thus,  528 

4 


10572 


12  2112 

1-0  shill.  =:  2 


^|0)12()8700iO  2.J*  6V/,     r=  0  50 

21l450cts.  2114  50 

Am,  5114  dolls.  .50  cts. 

To  change  Federal  maney  to  Canada  and  Xova -Scotia  currency. 

Rule.     Divide  tho  sum- in  dollars  by  4  for  pounds.- 

It  tliero  be  dollars  and  cents,  multiply  the  given  sum  hy  (>0, 

and  ihf  product  (rejecting  two  figures  on  the  right)   is  tiic  a.ri- 

»wcr  in  pence. 

Examples. 
1.    Change  144  dollars  to  Canada  eurrenc}'. 
4)144 

Ans.  £.30* 

r.    ^  liai^gf^  2114  (Iris.  50  ct^-.  to  Canada  or  Nova-Scotia  c?»r- 
ti^Mcy.  21  14.50 

()0- 


1»^ 


12)l2()S7C!0O 
C!0)1057t2— ft 

528    >2  S         An3.  £,oTi  112^.  ^d-.. 


42  COMPOUND  MULTIPLICATIONS', 

COMPOUND  MULTIPLICATION 

Is  the  multiplying  of  niiiirjcrs  oi'diiToient  denoi  viivition?,  by 
a  sis)V)!e  i-'j^awt  cm-  ligurcs  wiio^e  proiluct  shall  be  c(|iiul  to  a  pro- 
posed iraiiibc']-. 

I.  \Vheii  the  ((uantity  docs  not  exceed  1'?,  multiply  the  price 
by  the  (pj-mtity,  and  the  product  will  be  the  answer. 

JMultiply  £aQI      17     8i 
'bv  2^ 


Ans.   £.333      15      5  £Ad67      1^     O;^ 

£.980      J9      11^  £.'209      18     4i 

32  9^ 


I.  What  will  7  yards  of  shalloon  come  to  at  3s.  5(L  per  yard  ?• 

s,       (I. 

3     5 

7 

£.1     3   11 

s.  d.                              £.     s  J: 

x>.     4  lb.  tea ••    6"  8 I     ()  8 

3.  o  busbels  rye 5  9  1      8  .9 

4.  ()  gallons  wine    •.••    7  5  2     4  ()" 

5.  7  quintals  fish    . . . .  I9  6 6    \6  6 

i\     9  cwt.  iron     29  10  13      8  G 

7.  1 1  gallons  brandy »  •  •  •    8      5 >    12      7       - — ^ 

8.  12  quintals  lish 22    10   •  .- 13    14     0 

II.  If  the   number   or   quantity  exceeds  12,  and  is  to- ber 
found  in  the  table,  multiply  by  its  component  part::. 

Examples. 

5.     (J. 
i.    14  vards  durant  at     2     5 


4    10 

.       7 

Ans.  £.1    13   10 


COMPOUND  MULTIPLICATION.  4*1 

5.  (I  r. 

5.  l()  vnrcls  silk*  ^at*  •  • '4  9  

3.      20  lb.  coffee...- 1  9j  

4'.     28  gallons  rum ()  .^) ,:  • .  •  • 

.5.     4.5  cwt.  iron 2,9  ^)  •  » •  • 

6.  jOi  yards  broadcloth  2vi  7  .  •  •  • 

7.  0"3  pair  shoes 9  :)  •  •  •  • 

8.  84  quintals  Ijbh  ..••  is  (>  .... 

9.  100  oalls.  mclasscs  •  •    3  5.^  

10.  121  bushels  cm 4  3'  

11.  14 1  gallon-  »  .    5  I'l  


i 

1  ,> 

.'  u 

9 

1 

3 

(•() 

7 

(.; 

80 

0 

8 

29 

o 

9 

77 

14 

0 

17 

5 

lo 

25 

14 

40 

13 

0 

7'j  inuliii^Jif  l)!/  fracfionaf  f  !;■{■,  ;/?  .;,  ^;,  ~,  .:^  :•. 

Rule.  Multiply  the  price  by  the  upper  ligarc  ot"  tlie  frac- 
tion, and  divide  the  product  by  the  lower,  the  quotient  will  Le 
the  answer  ;  but  when  the  upper  figure  is  not  more  than  one, 
dividing  the  price  or  sum  by  the  lower  iigure  gives  the  answ.cr, 

•EXAMP.LES. 

1 .  What  is  3  CI  a  yard  of. cambric  worth,  aj:  i2s,  6d.  per  vard  ? 
\2     G 


Ans.  4/;.  8|(/. 

2.  What  is  Y   -fa  }aid  of  broadcloth  wo^ih,  at  35s.  p-r  ya: 
3  ■)  Or  thus,      2)33 


'  2)17  6  p ri ce  o f  liu ! (  a  }:! id , 

4-)  103  8  9  a  quarur. 


3.  One  quiirter  of  a  yard  of  fmc  linen,  at  Js,  6c!,  per  yard, 
'4)7     0' 


An-.    IsAOld, 

4..  Multiply  £A  5s,  3(L   hy  \,  or  take  h  ij(  it. 
3)4      3     3 

Ans,  £.1      8     5 


4-t 


COMPOUN^D  MULTrPLlCATION; 


5-.  Multiply  £,9  6s.   8iT.  by  |,  or  take  i  of  it^ 
9     6     8 
7 


8)6\>     ()     8 
Alls.  £.8     3     4^ 

JIT.  When  the  number  does  not  exceed  the  tabfe,  and  it  can- 
aot  be  found  in  it,  find  the  nearest  to  it,  either  less  or  greater  ; 
then,  after  having  found  the  price  of  this  number,  add  or  sub- 
tract the  value  of  so  nuinyy  as  it  is  less  or  greater  than  the  giv- 
en number. 


i'.XA-.MPLES. 


1.     27  bushels- of  corn,  at  4?.  lU/.  per  bushel.. 
4      11    ♦ 


9     6 
6 


8    17      0  price  of  36  bu>hel?.. 
4    1 1  price  of     I  buhhcl. 


An*.  <£'.S^      1    11  price  of  o?  bushels. 


9,  ITI  yards  siialloon' 'at- 

S.      ^3-1  li).coilee 

4.  o7o  galls,  ruin    

5.  ^1 }  yds,  baiz^'    •  •• 

6.  IOC)     oidntals  fish    

7.  137.1  gallons  of  molasses  • 


s^     J, 

•  2     8 

'    1    lO.'j 

•  2  r 
■  1 4  () 

•  3      Si 


£.    s,  (L 

Ans.   C!     ()  0 

2      4  Oi 

VI      1  llf 

9     ^3  94 

0  () ' 

()  1^ 


^'  9 
.1 A 


"U  the  number  is  above  the  taMe,    fh^.l   the   i^iicn  ♦^t 
as  ill  fhe  fullowina— 


COMPOUND  .^lULTirLICATION.  43 


Examples. 


I.   17s  yanls  of  iwuslin  at  4-.v.  5(7.  per  yarJ, 
4      .5 
10 


2     4      2 
10 


?2      1      8  price  of  rOO  yards.. 
15     p     2  price  of    70 
1    15     4  price  of      S 

AiiS.  .t..3i;     (j     2  price  <;f  178  yarik, 
2.  *284^  gallons  of  molasses,  at  Ss.  9^(1  per  gallon- 
10 


1 

17 

11 

10 

18 

19 

2 
2 

37   18  4    price  of  200  gallcns. 

15     3  4    price  of    80 

15  2     price  of      4 

1  10 1  price  of         J 

'    Ans  £ .53   18     8  j  price  of  28:^^  gallons, 

s.     <?.                                £.  s.  d, 

3.  1S3  galls,  iiin' •  •  •at 7     5    .•.•Ans.»«67  17  3 

4.  345  quii^l^i*^  ^^f  ^'-^^ ^3     9    ^1^^!)  13  i) 

5.  76"9|  lb.  ccffc^; I    10 70  11 

(>.     801}^  yards  baize., 2      ih"  - ^()  0  21: 

7.  23754  galls,  of  molasses.  •  3     5| 410   15     3.^ 

8.  Tliroc  barr(f{f^f  N.  E.  rum,  conty-iniug.  31,     32i 
33.^  gallon*,  at  4*'.  7i^A  per  gallon.  Ans.  ct'.22  7  ^| 

9.  Four  hogsiicads  of  molasj-es,  containing  [)? rj,  99ij  105|j 
and  1  I;i:l  gallons,  at  3-s.  8.-^fA  per  gallon,  arc  delivered  by  A  ro 
B,  U)  \sboyi  he  owed  258  dolij?.  It  is  required  to  know  the  ba'-. 
i'Awv.  an;]  'rv\\'l\Qse  favour  it  is  r     Ane^.  4?.  ihd,  in  favour  of  B.. 


» I 


^ina 


4(5  Cl>^\lPv)UNi)  JvIlLl  iPLICAiK 


v./.> 


Whorj  the  innoiinl  ofa  cwt.  >s  requiFcd  at  a  certain  ratepv^rnj. 
lluLi:.     Find  the  ])rico  of  one  or  two  quarters,  and  multipljf 
\lie  product  by  the  component  parts  of  a  cwt» 

1.   1  cvvt.  of  Flour,  at  .^..7.  per  lln 

3 
7 

14  0  price  Qf  Iwa  qtmvft^fi* 

Am.  £A     ^  0  price  of  om  cwt. 

Or  by  inverting  the  question  thu^, 

^    4  ihc  price  of  112  Vm,  at  Id,  per  Ibr 
3 

£a     B    0  the  price  of  112  lb.  at  Sd  per  lb. 

5,  Two  cwt.  Flour ':h  per  lb, 2     0'  8 

3,  Three  • .  Rice   '2^i  --......  .3  17  0 

4,  Four    •  •  Iron    •  •  •  •   S\  » » • 6     \  4 

5f  Five     •  f  Imligo  8.v.  i  1 4  .....*,.•.,,..  250   16'  8 

1.     What  will  4000  feet  of  boards  coiue   cO  at  38^.  Ad,  pej 
thousand  }■  1    18     4 

4  M. 

Aps.  £.7   13     4 

5,  3,5£/5  feet  of  boards  at  305.  per  tliousand. 

3b  In  ill!"  cxamn-e    Ihiro    fiL'nres    ^re 

m.,.  p.  irited  off   as  a    rciiniindcr,    and  thff 

21576'  lomlh  ii'duri'  of  »bo  prod\icl  of  this  re- 

107S8  rruiider,  nniltiplitHl  bv  I'i;   ;>;  <et  ''•- '^ 

^ 

>^///v.   1'2!),456 

Ans.  X.6'  Q  a 


COMPOUN D  ]>IULTIPLICATION,  47 

853  feet  of  boarc^s  at  SOy.  per  thousuud. 
853 
30 


chilh,  25,590 


-€.36 

6 

11 

64 

15 

6 

4 

16 

0 

4 

8 

9 

A-,^.  Sa      5  7 

4.  5,C?31  feet  of  3  inch  W.  O.  piank,  !2'255. 

5,  8,()37    ^i    •'       ••       '••     '  ^5t]6\ 

6*.        ,1)00 ^^ ]()0y. 

7.       ,888    2?>  pine,  ..         ••  ICOa'. 

Plank  are  sold  per  tlious.'u/J  of  'J J  iachfs,  tlie  usual  thickHcss  for  planking 
'.-.•hscIs,  mid  ii'i  there  are  geiieraUy  other dimenskms  as  2  and  3  inches,  lh« 
price  of  each  ii  regulated  by  the  price  of  the  '2-\,  adding  to  it,  or  subtracting 
l\oin  it,  in  such  pro])()rtion  as  may  be  agreed  on  uhcn  purchasing.  lii  the 
above  example,  taken  from  an  aciaal  '^ak^  -I-  of  I50s,  was  added  to  it,  for  th« 
three  inchj  and  J  Uedvtcted  from  It  for  llie  two  inch,  niuking  the  three  iiirM 
^^'■25s.  and  the  two  inch  100s.  per  thoi-jand. 

11  EIGHTS  AND  PLEASURES. 

fb.     oz.     diift.    grs.  Ih.     oz.    dv.f,      o-?-,^. 

Ihiltiply     14     9     14     17  825     8      1^     22 

by  5  8 

Troduct 


t   74   0   13 

13 

^605 

11 

10   8 

T,     CKt.    qm.     lb. 

19   17   3   25 

9 

Cn't.  qr. 

17  1 

lb. 
14 

oz.      drs. 

11  u 
7 

T.  hhJ.    gat. 

87  I  57 
5 

T. 

28 

p.  1 
I 

hhd.  gal. 

1  62 
7 

What  is.  the  weight  of  47  casks  of  rice,  each  weigliinir  2C. 
If/-.  23/i.  ?  Ans.   1 J5  cvvt.   1  qr.^  17  lU 


48 


COMrOUNI)  iMULTin 


X. 


BILLS  or   PAKCELS. 

)\\L  boi'g/-f  of  WiLiAA-Td  11ussj:ll, 
.- iit 4     o    


£a  16'    0 

-3      2    0  ]  5    ]  0 

14-      0    ..2  2      0 

4      '2    1  .5      0 

1      S    0  3     4 

7      6' 1  10      0 


^.7    12     2 

TorisnwutJi,  \£,ih  1. 

B  oug/i  I  of  S  m  o  i^  ^V  J  t  s  t)  N , 

i  I 4*.() ^'.0     7    ]  0^ 

>:  cc;in 5.^.4  .....e» 

/)     (iiuiiis  braiidy  • 8^.4  per  i!;<illGn    •••.•.. 

V        da,     luiii    v.^'.O         do.  


^'.3    1  I      0^ 


11  ( 


J!/r.  Am('?^  Gilts 


: .;  ^  >• 


12 


4 ••  -do.  • 

A. '.V    . 


£.2      5      G 


.1'.  I.S      7      0 
']'ru:d.  .  .  .  .  1      ^      O 


,t2  i :)    H      0 
65  d'jlU,  10--  eta. 


COMPOUND  DIVISION.  f9 

Natiiax  Perkins  Boston,  \Otli  August,  1803. 

Bought  of  G  K  0 11 G  E   A  E  L  E X  , 

6^\  yds.    striped  iiLinkins.  .at.  •    !25.    ct'.6     9     0 

v)'2  ells  mode '>v.    

28:^  yds.  calico     • -'•■^ 

2  grocc  gilt  coat  buttons ....  1  86.6 

3  pieces  russel  ••••••• 3  i^.    

£.21    10     () 


71  dols.  7-3  cUi. 


Af/-.  William  Sands  NcxdncnjpQvt,  Sept.  10,  1803. 

i>07/g^ ^  o/'  St  e  p  h  e  y  N  o  w  l  a  x  , 

2  pieces  muslin    30a\    X.3     0     0 

25  yards  Irish  linen  « 2^.    • 

28  J   do.  stormount  calico 'Is. 6 

28^   do.    .  •    red    •  •  •  •  do.      •  •  •  •    2 v. 2 

1  piece  duraut 5()6-.     

2  pieces  blue  shalloon •  *  67-^.6' •  •  • 

50|  yards  dimity '•  •    2s.6   • 

3  pieces persiasi •  S4i.      • 

£.y.O   12     3 


132  dols.  4  cts. 
Received  paymcr.t  by  liis    note,  of  the  above  date,  at    tlwce 
months.  For  ''''■■  ucn  Noiilun, 

ABRAHArj  Trusty, 


COMFOUND     DIVISION 

Teacheth    to   find  how    often   ©ne  number  is  contained  iu 
another  of  difl'crent  denomination^^. 

Examples. 
1.     Divide  £.19  U.v.  9.W.  by  2. 
e)19'l4'     9h 

Ans.  £S  17     ^l 
5.     Divide  £.900  11   9l>  ^y  3.  Ans.    -£.300  5   llj 

Prove  this  answer  to  be  right. 
E 


0  COMPOUND  DIVISION.    • 

3.  Divide  .€.1 '21   7s.  9¥'  ^n^  5.  Ans.  £.'2-1'  !y\s.  6|rf, 

4.  Divide  £.'24-8  5)^.  U^.  by  c).  Ans.  ^.27  12.>.  3^^ 
r^.  Divide  £.1037  1.^.  3^7.  by  12.  Ans.  £.88  1.9.  9|d 
II.  If  the  divisor  exceeds  12,   and  it  be  found  in  the  table, 

divide  by  its  component  parts. 

Examples. 
1.     Divide  £.278   S^.  ^d.  between  45  men  equally. 
5)27  8     8     9 

S)oo    13     9 


Ans.  £.6     3     9  each. 
^.     If  20  lb.  of  indigo  cost  £.7   5^.   10c/.  what  is  it  per  lb.  ? 

Ans.  7'^.  o\(L 

3.  If  21  yards  of  durant  cost  62s.  Gd,  what  is  it  per  yard  : 

Ans.  2s.  7 id. 

4.  If  72  bushels  of  corn  cost  £.20  9a\  6(/.  what  is  it  p<?r 
Lu.hcl  ?  Ans.   5s.   8  J  J. 

5.  If  108  lb.  of  tea  cost  £.45  13-y.  6J.  what  is  one  pound 
w^orth  ?  Ans.   8^.  5kd. 

6.  When  £.\66  I3s.  4J.  is  paid  for  500  gallons  of  rum, 
what  is  it  per  gallon  .?  Ans.  C)s.  Sd. 

7.  If  lOod  gallons  of  molasses  cost  £.209  7s.  ()t/.  what  is 
it  per  gallon  ?  Ans.  4,9.  2.|r7. 

III.'  If  the  divisor  cannot  be  found  by  the  multiplication  of 
small  numbers,  as  the  preceding  examples,  divide  by  it  as  in 
the  following  Examples. 

J.     Divide   £.46  Is.   lU/.  by  37. 

£.    $,     d. 
37)46  1  ll(r'4  11  Ans. 
37 

9 
20 

37)181(4 

148 

33 

12 

37)407(11 
37 

37 
37 


•COMPOUND  DIVISION.  5i 

e.    ^Divide  i^.53    \3s,   f^Ul,  by  23^  Ans.     £l  9  3h  ' 

3.  *if  34-5  quintifls  uflish  cobt  X'.4:09  Xos,  Qd.  how  much 
is  it  per  quintal  ?  Ans.  Qos.  Qii. 

Dividing  by  fractional  parts,  ars  .^,  -',  ^^,  <5cc."is  the  same  as 
multiplying  by  the  in.  Soe  tlie  Rule  under  Case  IL  in  Com- 
pound Multiplication. 

1.  Mow  much  is  ^  of  £.91   Ha'.  3f/. 

91   11     3  Or  thus     2)91   1 1     3 

3  

•  ■  2)45   15     7J  one  half  the  sum, 

4)274   13     9  22   17     9|  one  quarter. 

Ans.  £68   13     5j  £M  13     5|  answer. 

2.  Divide  £.126  19^.  5Mbyf.     Ans.    £.101    11     7 

3.  If  the  wh©Ie  of  a  ship  is  worth  £.960  what  is  f  worth  ? 

Ans.  £M0 

4.  If  I  of  a  ship  was  sold  for  £.1056  2^.  Id.  what  was  the 
whole  valued  at  ?  Ans.  £.16*89  15     4 

IV.  Having  the  price  of  a  hundred  weight,  to  know  how 
much  it  is  per  pound. 

Rule.  Find  the  price  of  1  or  2  quarters,  and  then  divide 
by  the  component  parts. 

1.  If  1  cwt.  of  steel  cost  £.4.  6s,  4cf.  what  is  it  per  lb.  ? 
4)4     6     4  Or  thus     2)4     (3     4 


4)1      1     7  price  of  1  qr.      7)2     3     S  price  of  2.  quarters. 


7)0     5     4|  8)0     6     2 


Ans.      0     0     9}  per  lb.  0     0     9}  per  lb. 

2..  ''^  1  c^Yt.  of  flour  cost  23^.  4J.  what  is  it  per  lb.  ? 

Ans.  '2hL 

3.  When    2  cwt.  of  sugar  cost  £.8   17^.  4(/.  what  i^  it  per 
li'.  ?  Ans..  g^d 

4.  If  5   cwt.  of  ij'on   cost   £.8   15^.  0^/.    how   much  "is   it 
per  lb.  ?  Ans.  3^d, 


1.     A  mate  and  3  seamen   have  to  receive   6OO  dollars,  for 
i^pturing  their    vessel,    ofwliich    the  mate  is  to  have   twOi 
snares  and  each  seaman  one  share;  how  much  is  the  part  CI" 
<*'^<-"^i  '  Ans. — The  mate's  part  is  240  dols. 

and  each  scamaii*s  120^ 


52  DECIMAL  FRACTIONS. 

'2.  (^jipt  31.  of  the  Jasgn,  meets  at  sea  with  tlie  w 
tli.^  Hiiwk,  of  Boston,  I'rom  which  he  takes  sundry  aiiicios^ 
whicli  hill  for  521  dollars  64  cents  :  two  tliirds  of  this  sum  is 
Mwaidv'J  to  the  owners  of  the  Hawk  ;  of  the  other  ■  :;,  ■  owii;- 
t  r>  rl  tiie  Jasoa  are  to  have  ^-,  and  the  remainder  i><  tr»  be  di^ 
vide  J  between  the  captain,  mate^and  nine  seamen,  aihjwing  the 
captain  3  shares,  the  mate  2,  and  the  seamen  1  share  each  ; 
what  is  the  respective  part  of  those  concerned  ? 

dols.  c(i>. 

Ans. — The  owners  of  the  Hawk     347  76 

owneis  of  the  Jasoa       86  94f 

captain  ............    18  ()3 

mate* • 12  42 

each  seaman ........     6  2i 


DECIMAL  FRACTIONS. 


A  DECIMAL  FRACTION  is  that,  whose  denominator  is 
an  unit,  with  as  many  cyphers  annexed  to  it,  as  the  numerator 
has  phtCes,  and  is  usually  expressed  by  writing  the  numerator 
oniA,  \\i;li  a  point  before  it,  called  the  separatrix  ;  thus,  j-^q, 
lou^  iVtAi?  ^^'^  decimal  fractions,  and  are  expressed  by  ,5  ,'^5 
,125  respectively. 

The  fissures  to  the  left  hand  of  the  separatrix  are  whole 
numbers  ;  thus  4^5  yards  is  4  yards  and  5  tenths,  or  one  half 
of  another  yard. 

Cypliers  placed  to  the  right  hand  of  decimals  make  no  al- 
tei.tl:  11  in  their  value;  for  ,5  ,50,500  <i'C.  are  decimals  (f 
th-'  ^-..inc  value,  beini^  each  equal  to  5  ;  but  v\  hen  })laced  to  the 
left  hand,  tlie  value  of  the  fraction  is  decreased  in  a  tenfold 
]ji"por{iun  ;  thus  ,5  ,05  ,00.)  tVc.  are  5  tenth  parts^  5  liuiv- 
dredth  parrs,  5  thousandth  parts,  re^pc(;tivcly, 


DECIMAL  FRACTIONS.  53 

The  diiTorent  value   of  fjgiires   will  ^appear  plainer    hy  tho 
f()l lowing  '     .  :y 

TABLE, 


In  T  KG  K  us. 

Decimals. 

o 

^ 

■^7 

2  0 

o 

2  0  0 

.0 

2 

2  0  0  0 

,0 

0  2 

2  0  0  0  0 

,0 

0  0  2 

2.  0  0  0  0  0 

,0 

0  0  0 

n 

2  0  0  0  0  0  0 

,0 

0  0  0 

0  2 

2  0  0  0  0  0  0  0 

,0 

0  0  0 

0  0  2 

2^000000  0  0 

,0 

0  0  0 

0  0  0 

2 

o 

r-      C-"    ^ 

S  5.  2 

^ 

D 

Hi   o    •-■ 

£ 

en 

^S  s- 

E-  ^  ;- 

^ 

O-    -Ti  3    o    "-^  S    o 

• 

f^  E;  c 

c    5    "■ 

W5       -J       •          !/3       —    CL,    Cfl- 

o   ^       o   o   • 

^  :::t  E: 

■^     V)      p 

'^' 

•■  w  ^ 

o        j::^. 

rr:  '          s^   JIT* 

1" 

p 

o' 

'''iora  this  table  it  appears,  that  as  whole  numbers  increase  in  a  tenfold  "{>m-- 
loa  iVom  units  to  the  left  hand,    so  dechnals  decrease  in  th,e  same  j>roiior- 
t.ou    U)   the  right — and  that  in  decimals,  as  in  whole  numfccivs  tli:  . 

frgure  d-iterraines  its  relative  vahre. 

ADDITION  OF  DECIMALS, 

IluLE.  Place  the  given  numbers  so  that  the  decimal  points* 
m::;/ stand  directly  uudoi'  each  other,  then  add  as  in  whole 
liunibers,  and  point  off  so  many  places  for  decimals  to  x\\&..- 
rii^ict  a.  wvc  equal  to  the  izreatest  number  of  lli€  decii-n:d  plaCOft-. 
iL  .  .:■  given  nunr-ors. 

':  -..'>r  4?,':3  2,1 

11,^:8  ^%,A7  ,5 

3S-k39  5::, 384.  .? 

1^9,^^  2,1  .>■ 


ijO:^0, 


E2 


l^i,-iS4»- 


'd^iW 


^^  DECIMAL  FRACTIONS. 

RGqiiired  the  sum  of  fep^enfy-nine  and  three  tenths,  three 
liundred  and  seventy-four  and  nine  miilionths,  ninety-seven  and 
TWO  hundre«l  and  iifty-three  thousandths,  three  hundred  and 
litteen  and  four  hundredths,  twenty-seven,  one  hundred  and 
iuur  tenths.  Ans.  942,9^3009. 

Required  the  sum  often  dollars  and  twenty-nine  cents,  nine- 
ty three  cents  and  three  mills,  nine  cents  and  six  mills,  and 
two  duilargand  eight  mills.      Ans.   13  dols.  32  cts.  7  mills. 


SUBTRJCTIOJSr  OF  DECIMALS, 

Rule.  Place  the  given  numbers  so  that  the  decimal  points 
may  sta'ul  directly  uncier  each  otjier,  and  then  point  off  the  de- 
cimal places  as  in  addition. 

Examples. 
From  219,4-2  87,26  57  311 

'Jake    184,38  19,4  9,375  11,11 


35,04     ,  67, 8()  47,625  299,89 


From  two  thousand  and   sixteen  hundredths  take  one  thou- 
banii  and  four,  and  four  miilionths.  Ans.  996,15^)996. 

From  twenty-four  thousand  nine  hundred  and  nine  and  one 
teiitli  take  fourteen  thousand  and  twenty-nine  thousandths. 

Ans.   10909,071. 

Tnkc  oiiihty-five  and    seven  hundred  and    thirty-seven  thou- 
saiuiths  from  one  hundred.  Ans.    14,263. 

From  five  hundred  and  thirty-one  dollars  two  cents  take  one 
hundred  and  seventeen  dollars  three  cents  and  four  mills. 

Ans.  413  dois.  98  cts.  6m. 

MULTIPLICATION  OF  DECIMALS, 

Multiply  exactly  as  in  wiiole  numbers,    and  from  tli(^  product 
rut  off  as  many  figures  for  decimals  to   the  right  hand  as  tlicre 
- -o  ?i(M'imals  in  both  t!ie  factors,  Ijut  if  the  product  should  liol 
.;  nvany,  supply  the  defect  by  prefixing  cyphers. 


DFXIMAL  FRACTIONS.  55 


^Multiply     36,5 
by        7,27 

Examples. 

29,831 
,952 

3,92 
19^' 

2555 
730 
2555 

59662 
149155 
26'8479 

2352 
3528 
392 

oduct       265,355 

28,399112 

,285 
,003 

768,32 

Multiply          ,2S5 

,29              124 
,1                ,06 

Product     ,2280 

,000855 

,029             7,44 

Note.     To  multiply  dccim-il  fractions  by,  10,    100,   1000,   &c.  is  only  (• 
reaiove  the  separatrix  so  many  places  tovrards  the  right  as  there  are  cypheri»» 

Thus;  7,3G2937  rio     -)     r 73,62937 

,    .     V      ,    ,  1   IOC)         f     .       1736,2937 

n^ultipnedby   J^^^    ^  ^^  S  7362,937 

(10000  3    (73629,37 

Multiply  twenty-nine  and  three  tenths  by  scvent^n. 

An?.  498,1 
Multiply  twenty-seven  thousandths  by  four  hundredths. 

Ans.   ,00108. 
Multiply  two  thousand  and  four  and   two  tenths  by   twenty- 
seven.  Ans.  54113,4 

PRACTICAL  QUESTIONS. 

1.     How  much  will  93  yards  of  shalloon  come  to  at  53  cents 
per  yard  r  '  *^^^^^  / 

9^ 
,53 

L 


279 
465 


49,29  Ans.  49  dolls.  29  cents. 


2.     At  21  cents  9  mills  per  lb.   what  will    1S7  lb.  of  cofice 
come  Vj  ?  Aiis.  40  duls.  9^  cents  3  mills. 


bG  DECIMAL  FRACTIONS. 

3.  ^Vliat  will  27  cwt.  of  iron  come  to  at  4  dollars  56  cent:* 
per  cvvt.  ?  Ans.   123  dols.  12  centL>. 

4.  How  much  will  281  yards  of   tape  come  to    at  9  mills 
per  yard  ?  Ans..  2  dols.  52  cents  9  njills. 

5.  What  will  371  yards  of  broadcloth    come   to  at   5  dols-. 
79  cents  per  }ard  ?  Ans.   2148  doh.  f)  cents. 

6.  How  much  will  29i  yards  of  mode  come  to  at  75  centii- 
per  yard  ?  Ans.   22  dols.  12  cents  5  mills. 

7.  Wliat  will  23,()25  feet  of  boards  come    to  at  8  dollar?, 
^j  cents  per  M,  ? 

23,()25 

118125 

47250 
IS^OOO 

104,^0625  Ans.   Ipi  dols.  C)0  cents  ^min«^. 

8.  How  much  will  712  leet  of  boarcis  come  to  at  14^ dollar: 
per   the  usand  ?  Ans.  p  dois.  £i6  cents  8  n)iHs. 

f).     What  will  25,6'50  fc^ot  of  clear  boards  come   to  at   17 
dols.  50  cents  per  thousand  ?     Ans.  44S  dois.  87  cents  5  mills. 

Lois.  Cts.  Do'.s.  Cts-  M. 

10.  15,859  feet  clear  boards  * ' » -  17   50  per  I\I.     277   53  2 

11.  812 •- do.   •.   14-       -..    11    36  H 

12.  37 ^'   • do.  .  .   12   75  » •  •      4  75)  4 

13.  3 1,49()  merchantable     do.    •-    8        251   9^   8 

14.  269 do.-'      (;75 1    M    :- 

15.  4,114  reliisc    do...      3   37 13    80   4 

16.  393  maple d;>.  -.  8  per  i\ot      31    44 

17.  57  nnihogany    •• ^  32        (!>-.   ••    18   14- 

18.  195  ;:allons  nu)lasscs  ....  57  pc  :•;.:.■! .    Ml    15 

19.  1 6:)     do.      vuin      .......  9'3    175  77 

20.  2'i3  yards  laize       23  |  er  yard    55   89 

21.  197  feet  clear  boards  ... .  2  j.er  foot        3  94- 

DIVISION  OF  DECIMALS. 

TrTK.      Dixile  as  in  whd^'    rii;.;^--r-,   nnd    fiMn 
-.■1.  .^;neiit   pc' 

ihc  >U\- ; J. luces  in  th 

Ijt'  the  places  of  the  (pi 

quires,  siippsy  tire  deie<.  i  .-.   ;      .: ,., 

tkere  be  a  rcuiaiixdcr.  or  the   dccihud  • 


DECIMAL  FRACTIONS.  .  57 

more  than  those  in  the  dividend,  cyphers  may  be  annexed  to 
the  dividend,  and  the  quotient  earned  to  any  degree  of  exact- 
ness. 


9^),S53972(,009391 
8^8 

E: 

'CAMPLES. 

,853)89,000  (104,337,  ^c. 
853 

3^9 
270 

3700 
3412 

837 

828 

92 

2380 
2559 

3210 
2559 

6510 

5971 

539 


The  various  kinds  that  ever  occur  in  division  are  included  in 
the  following  cases,  viz. 


Divide  ,803 

by  ,22 

Ans.  3,65 

,806 

2,2 

,365 

,803 

22 

,0365 

80,3 

,22 

365 

80,3 

2,2 

36,5 

80,3 

22 

3,65 

222 

,365 

608,21 -f 

222 

3,65 

60,821 -fn 

222 

3^5 

,6082 1  4- 

As  mulrip'ying  by  10,  100,  1000,  &c.  is  only  removing  the  separating 
pojrH  of  the  muliiniicand  so  many  places  to  the  right  hand  as  there  are  cj* 
phers  ill  the  mnltiplior,  so  to  divide  by  the  same,  is  only  removing  thesc|)a- 
Irdtjrix,  h\  vUq  same  manner  to  tUe  left. 


5a'  DECIMAL  FIIACTIONS. 

PRACTICAL  QUESTIONS. 

1.  When  butter  is  sultl  ar  12  cents  8  mills  per  lb.   how  lua* 
X^y  lb.  mi!}  be  bought  for  224'  dollars  ? 

,12S)221<,000(1730 
12'8 

640 

640  Ans.  17501b. 

Here  the  cypTiers  annexed,  to  the  dividend  bemg  equal  to  the  decimal 
places  in  the  divisor,  the  quotient  is  a  whole  number. 

2.  If  673  bushels  of  wheat  cost  786  dols.  73  cents  7  mills* 
what  is  it  per  bushel  ? 

67  3)7  S6,7  37  {1,169 
673 


1137 
673 

4643 
4038 


6057 

6057  Alls.  1  dol.  16  cts.  0  mills* 


In  this  example,  as  the  divisor  is  a  whole  number,  three  places  are  pointed. 
4)iF  in  the  quotient,  to  equal  those  in  tfie  dividend. 

3.  If  493  yards  Cost  4  dols,  43  cents  7  mills,  what  is  it  per 
yard  ?  Ans.  9  mills. 

4.  If  125  gallons  of  molasses  cost  9-5  dollars,  what  is  1  gal- 
lon worth  ?  Ans.  76  cents. 

5.  If  205  yards  of^durant  cost  107  dollars  62^  cents,  what 
is  it  per  yard  ?  «  '  Ans.  52|  cents., 


•   "DECIMAL  FRACriONS,  5^ 

REDUCTION  OF  DECIMALS. 
Case  I. 

To  reduce  a  tuIgHr fraction  to  its  cquixakiit  decimal. 

KuLE.     Divide  the  numerator  by  the  denominator,  and  the 
quotient  will  be  the  decimal  required. 

Examples, 
1.     Reduce  £  to  a  decimal. 

4)3,00 


Ans.  ,75 

What  is  the  decimal  of  h  ? 

Ans. 

,5 

What  is  the  decimal  of  \  ? 

Ans. 

/^5 

What  is  the  decimal  of  f^  ? 

Ans. 

,15 

^Vhat  is  the  decimal  oi  \\  ? 

Ans. 

,68 

Express  |  decimally. 

Ans. 

,^7^ 

Case  II. 

To  reduce  numhers  of  different  dcnorninations  to  their  equivaknt 
decimal  values. 
Rule.      1.    Write  the  given  numbers  perpendicularly  under 
one  ancither  for  dividends,  proceeding  orderly  from  the  least  to 
tlie  greatest. 

2.  Opposite  to  each  dividend,  on  the  left  hand,  place  such 
a  number  tor  a  divisor  as  will  bring  it  to  the  next  superior  name, 
and  draw  a  line  between  them. 

3.  Begin  with  the  highest,  and  write  the  quotient  of  each 
division,  as  decimal  parts,  on  the  right  hand  of  the  dividend 
next  below  it,  and  the  last  quotient  will  be  the  decimal  sought. 

Examples. 

1.     Reduce  14^.  5ld.  to  the  decimal  of  a  pound. 


4 

2 

12 

5,5 

2X) 

14,4583 

Ans.  JQ^g 

2.  Reduce  15  shillings  to  the  decimal  of  a  pound,  Ans.  ,75 

3.  Reduce  3  qrs.  18  lb,  to  the  decimal  of  a  cwt. 

Ans.  ,910714  + 

4.  Reduce  2  qrs.  2  nails  to  the  decimal  of  a  yard.  Ans.  ,()25 

5.  Reduce  14  gals.  3  quarts  to  the  decimal  of  a  hdgshoad. 

Aus.  ,2341  + 


<)0  DECIMAL  FRACTIONS. 

Case  IIL 
Tojind  the  decimal  of  any  number  of  ii  hillings, 'pence  and  farthings^ 

iij  ini,p€ciion. 
Rule.  Write  liaif  the  greates;  c\cn  number  of  shillings  for  (lie  first  de- 
ciniai  iiLTiire,  aiifi  h:X  {!'t>  lar!l!ii.i;s,  ii  rhe  ^iven  pence  aivl  iarihiiiiis.,  yx^'^'^ess 
the  >ecoiiv!  and  liiird  j>Ii:ces  ;  "'  sorvin^  \o  increa;?e  the  second  ])lace  by  :y,  if 
the  !s!iii:ings  be  odd,  and  tlie  lin;d  piace  by  1,  when  ilie  farthhigs  exceed  12, 
<ind  by  2  \viien  they  exceed  o7. 

Examples. 

1.  Find  the  (kcimal  oi  13a\  C)|(/.  by  inspection. 

,6       half  of  126'. 
5     for  the  odd  bhilling. 
39  farthings  in  <)^d, 
2  for  excess  of  37 

>691 

2.  Find  by  inspection  the  decimal  of  15^.  Sid.  ()s.  3ld.  ]Qs^ 
6^d,  3s.  6d.  and  2s.  ll^d,         Ans.  ,784  ,465   ,978  ,\75  ,148. 

Case  IV. 
Tojind  file  xaluc  of  any  given  decimal  in  the  terms  of  the  integer, 
Kui.i;.      1.     Miihijily  (he  decimal  by  the  niimber  of  parts  in  tlie  next  less 
deiioininaioii,  and  cut  off  as  many  places  for  the  remainder  to  the  right  liand 
as   there  are  places  in  the  given  decimal. 

'2.     JMultiply  the  remainder  by  the  parts  in  the  next  inferior  denomination, 
«.nd  cut, oil  a  remainder  as  beloie. 

3.      Proceed  hi    this  manner    througli  all  the  parts  of  the   integer,  and  the 
-several  denominations,  standmg  on  the  left  hand  make  the  answer. 
Examples.  , 

1.     Find  the  value  of  ,691  of  a  pound. 

,()91 
20 

13,820 
12 


9,840 
4 


3,360  Ans.  \3s.  9jd 

H.      Vv  i;at  i^^  the  value  of  ,9  of  a  sbillini^  .?  Ans.   10|r/. 

3.  \V]::.t  is  the  value  oi  ,592  of  a  cvvt.  ? 

Ans.  2  qis.  10  lb.  4  oz.  13  4-drs. 

4.  V,  !.al  i:   t'  :•  value  of  ,258  of  a  tun  of  wine  ? 

An?..    1  hhd.  2 -|- galls. 

5.  v......  .  -aliie  of  ,12785  of  a  year? 

Ans.  46  days   15  hours  b7  n)inutes  57 -f  see. 


j             Di  ciMAL  Tabits  oi  COIN,  WEIGirr  AND  MEASURE. 

Giiiinr,. 

j          LfliitnniS. 

TABLE  r. 

TABLE  II L 

6    * 

5 

1      ,ot:'5 
;()';o4i6 

English  Coin. 

TllOY  \Vl K.H  r. 

4 
3 

1       ,(K'0333 
,0'06v5 

1/.  the  Integer. 

1  U).   llie  liite-er. 

2 

1 

,004  1 66 

Sh. 

itr. 

^/Y. 

r/-.  C-. 

19 

,9,5 

9 

,45 

Ounces   the  sa:nc   as 

'i  ;:i  '. 

;,..       iv. 

1[) 

,9 

8 

,4 

Potee  in   the  Lst 

V 

,05 

7 

,35 

'Jabio. 

Avoiiujrrois  Vv^t.     | 

If. 
lo 

,8 
,75 

6 
5 

,3 

,25 

ilQlb. 

I  he  Iiitegcr. 

Penny 

Vt'cbiiuLs. 

1^ 

l.S 

,7 

4 

3 

o 
,15 

irti^l.'t. 

10 

,011666 

ll 

>G 

2 

,1 

9 

,037  5 

Q.s. 

Drchaah. 

11 

,55 

1 

,05 

8 

,033333 

3 

,7  5 

K; 

,5 

7 

,029166 

2 

,5 

i't'»CC. 

6 

,025 

1 

,25# 

6 

5 

' 

5 

,0,0833 

r; 

/)i()iJ./3 

4 

,0-i  C666 

4 

,016666 

:] 

,0125 

Pi-':: 

3 

,0r-^5 

2 

,008333 

14 

,11.3:»:i     \ 
,107  113     '• 
,0:"l,->i4 

t^ 

,O0B3.13 
,004166 

1 

,004166 

13 
12 
U 

1 

3  2 

Lee  una  Is. 
,002083 

i'.</( 

h." 

Dcciiniih. 

3 

,00.3125 

It 

,001910 

10 

/■'.i'jI?)G 

2 

,0:;-'(i[].3.3 

10 

,001^36 

0 

..  .;').;:-,r 

1 

,noio-n.s 

9 

,OC)L562 
,001389 

f} 

' 

8 

7 

TABLE  II. 

7 

6 

,001215 
,001042 

6 
5 

,0.k574 

,01  jc:;; 

Eng.  Coin.       1  57u7/. 

4 

,000868 
,000694 

4 
.3 

,0357  14 

L0N(^    I\ll  AS.       1    Foot. 

3 
«2 

,0(/0521 
,000347 

2 
1 

,oi;3i;.3    ^ 

The  Tr.k-cr. 

1 

,000 !  73 

II 

.  1  cr.  tlic  Lilogcr. 

8 

Dccir.urs. 
,'n)4;(-4     : 

Pence 

Decunuls. 

ani 
Inches. 

Penmnoc}jj!;ht  the  sa?nc 

7 

,^"o.>:o6    i 

as  ShiUin2;s  in  the 

6 

,0(.3343     ■ 
,0i;2?90     : 
,00t.'2:>2: 
,0. "^11674     1 

,416666 

,o.>.j,j33 

6 
5 

4 

first  Tab|e. 

5 
4 
3 

3 

/:5 

GraiiiS. 

Decimals. 

2 

,001116     : 

2 

,U)66^":6 

12 

,0'j5 

1 

,(.'C0558 

1 

,()8').:,3J 

11 
1) 

,022916 
,020833 

Fartii. 

7J('cv;ra?;,s. 

.1.  , 

3 

,0625 

9 

,01875 

3 

,^--.Mj<r   ( 

2 

,041 66  v'S 

H 

,016666 

2 

,or.0/r9    1 

^ 

,020833 

7 

,0145^.3 

1 

.O^^'^IS^i     * 

F 

T      •'^**'**-^ 

i> 

s„:,:K' 

(:.    '^■. 

J  'M  /;,,•, '/s. 

t   t. 

i  A  (•','/.             /V/.     ' 

iW 

y^.i:  \. 

.") 

,01 '.'ail 

o 

.  w ')            2 

'1 

,oi;,87-3 

i 

,1-5          1 

A>, . 

\Vt. 

'2 

,011904 
,007936 

1  ll>.  I 

■c  iii-.ogcr. 

1 

,003968 

Q.pt. 
3 
2 

Dcci:ti. 

,0937  5 

;0(iV5 

Ph. 

2 

Cz. 

Jhr^ymds. 

r/)r,'.s. 

]Jccin>uh. 

1 

,031i^5          1      1 

8 

7 

4 

,0019C4 
,001488 

6 

^''■75 

2 

,0-00992 

j;a^vH//5. 

Q.vhs. 

5 
4 

1 

,00r:4pf^ 

,0234;;75 

3 

2 

o 

,i;;7  "i 

A  bnns!)cai  ibe  Integer. 

,0078125 

1 

2 
1 

Ooo. 

V.'cinKils. 

30 

^0 

,476190 

Dccinnih. 
,   I.  )859 

Pis. 
.3        ■ 

VrrnT 

Decimals. 

10 

,1.^8730 

,(,03906 

2 

8 

,0:31;?;5 

9 

,1 J  2857 

,001953 

1 

7 

,o^i'^::'l:] 

8 

,126984 

6 
5 

,019^^'31 

7 
6 

,111111 

,0952>"8 

4 

,0156-^5 

5 

,07  9365 

TABLE  VIII. 

S 

,01  i7J8 

4 

,06;>J92 

o 

,007  ai  2 

3 

,04  7619 

Long   Mf.asure. 

1 

,003906 

2 

,031 7 '16 

1 

,015873 

1  MUe  iLe  Integer. 

TAl 

LE  VI. 

P///rs. 

Dccinui's. 

Yarrs. 

Decimals. 

LroL-iD 

TJeasure. 

3 

,005952 

1000 

,56818'^-, 

2 

,003968 

900 

,511364 

1  7^</ji 

ilic  Integer. 

1 

,001684 

800 

,454545 

700 
600 

,;-97  727 
,310909 
,284091 

G.-.'.. 

.D:r.-;,.'a/s. 

1i)0 

,r,9iy.v>.^ 

TABLE  YIL 

-iro 

,227:j7v 

?■) 

,:.:)7]  J I 

300 

,1704  54 

of) 

AlrAfURr:. 

100 

J  13636 

7.) 
(^  ■ : ) 

/,^7 

1!0 
90 

,056818 

,«.  151136 

o) 

,\<ji:\  \2 

Liquid.    •       Tr^/. 

80 

,04  5454 

d) 

,i.')8r;'o 
,1  V^n]7 

1  Cw'7..-?/.       1  Quarter. 

70 

CO 

,',"39773 
,0.  4('91 

^0 

50 

,(v.  ,'M09 

10 

Inlcgfr. 

40 

,()V27'-.7 

1) 
1  a 

[()3\T1G 

30 
20 

,017015 
,01  1364 

r^ 

Dt.r/w2. 

Fu. 

7 

,027 

4 

,5 

4 

10 

,005681^ 

6 

jO'foBOO 

.'3 

,r^75 

f] 

9 

,005111 

!                              .   AKL) 

s  or  COIX, 

WKiGii; 

' 

"i  ./..  .s. 

iv\  ci^uais. 

Vccuiiiil^. 

i 

/u)i:>4:) 

,0i>191» 

7 

,0;)oy77 

,0i'.n78 

1 

6 

,0!):vl09 

() 

,r  "6  i.io 

( 

1 

5 

,00:811 

5 

,()lS(:9d 

i 

'] 

/■rJ-,7.> 

1 

,oiu<=;)9 

1    ;■.,, 

2 

o 

/)')vr:9 

(■ 

1 

/yjO.nVo 

1 

,()■-):/  J9 

l\-i't. 

j_,-;,,;       /j. 

1   ;.'.;.  .,, 

:.itb. 

2 

,0i-0;j?8? 

o 

,  1  :•> 

1 

,0001894 

Hours. 

Dccim:ds. 

1 

,06  i  J 

12 
11 

,5 

,'{.)8333 

/jifVi". 

Decimals. 

10 

,416666 

TABLE  XI.          I 

6 

,{H).K)947 

9 

,37.> 

5 

/»00i)79 

8 

,,'>  )o33') 

L I .  A  D      A 

Vi'.icriT. 

4 

,000)6  51 

7 

/291G66 

r, 

,000:)474 

6 

/^o 

1  I\>tJ^a-  t 

ic  liilcgcr- 

ii 

,0000319 

5 

,908333 

1 

,00001.53 

4 

,166666 

IlunU. 

D'.rJmab. 

o 

1 

,1  :5 
,041666 

10 

9 
8 

,.')128-'0 
,4  6  i. -138 
,410-256 

TABLJ^^IX. 

% 

■V 

7 
6 

,358974 
,307692 

Time. 

Mi)!Htcs. 

Dccimiils. 

5 

,'25'HlQ. 

1  r.",/)-  thn  Integer. 

o) 

,0j()L],;3 

4 

,^05: 28 

iiO 

,013838 

,15384() 

f-i^uc     as 

10 

,o;;-6':m4 

o 

,102561 

tUi  s.co/r! 

9 
8 
7 
6 
5 
! 

,o;)6j5 

,005:>o5 
,004861 
,004166 
,003472 
,002777 

1 

,05r28'i 

I,;  s. 

IjLCinuils. 
,025641 

1 

.012020 

])r,:s. 

Decimals. 

L'ouu,.^. 

i.t'ciiuals. 

oiii 

1,00000;) 

,00i'083 

'       11. 

,C064iO'-2 

;•  •() 

,8lM91iS 

,0013  {JO 

13 

.   ,005952:; 

V  '.) 

,51794;) 

i 

,000694 

1! 

,r:05;9l5 

1  ■() 

,'.'7r>9;:> 

,VJ()  )75 

11 

1  ) 

,('0503(:6 
,00^157  87 

i\:) 

/,' 19178 

i) 

,O04r20h' 

7') 

,l9i781 

• 

8 

,003663i» 

C  ) 

,|{M;)H.> 

7 

,00.;'3v)51 

.^0 

,i.;6'.>::(; 

() 

,0O'27  47i' 

4  ) 
o  ) 

,');jji--> 

1 

,0022893 
,0018315 

1.:) 

,0:)179l 

3 

,00K)736 

]  > 

,o'j-.s;7 

,0009 ! 57 

o 

.O.Mo  .7 

1 

.  .0  -n-iV/!' 

€l'  SINGLE  RULK  OF  THREE  DIRECT. 

lyic  Single  Rule  of  Three  Direct, 

'inclo  Rulo  of  Three  Direct  teaches,  froiii  three  num- 
i  to  lind  a  fourth,  that  shall  t)e  in   the   siiir.c    pr(ipor- 
th)\\  io  ;!>e  liiird  as  tlie  second   is  to  the  first. 

\i  r:;orc  requires  7narCy  or  less  requires  less,  the  proportion  i%. 
direct. 

Rui.K  1.  I\Take  the  number  that  is  the  demand  of  tiie  ques- 
tion, the  third  term,  the  number  that  is  of  the  snmc  name  or 
(raality,  the  first  term,  and  the  remaining  number  will  be  the 

Ir^L  and  third  numbers   into  tlie   same,  fund  the 
>  1    vi^vt.  dciioraination  mcniioned. 

lid  and  third  numbers  toireilier,  and  di- 
vide'the  piuiUict  by  the  tirLu,  and  the  quctient  (if  there  be  no 
remainder)  is  the  answer,  or  fourth  number  required. 

If,  after  division  there  be  a  remainder,  jcduce  it  to  the  next 
denomination  below  that  to  which  the  seccnd  number  was  re- 
duced, and  divide  by  the  same  divisor  as  before,  and  the  quo- 
tient will  be  of  this  last  denomination.  Proceed  thus  with  all 
the  remainclers  till  you  have  reduced  them  to  the  lowest  denom- 
ination, which  the  second  number  admits  of,  and  the  several 
quotients  taken  together  will  be  the  answer  required. 

The  method  of  proof  is  by  reversing  the  question. 

Examples. 

1.   If  2  yards  of  cloth  cost  4-5.  what  will  12.>  yards  come  to? 

yd.s.     s.        yds.  yds.        £.  s.       yd'^. 

If  2:4::  ^125  Proof  if  "l25   :    12    10  :  :^  2 

4  20 


2)5CO  250 

, ^  2 

20)250 


125)500(1 
An-.     £A2    10  500 


SINGLE  RULK  OF  THREE  DIRECT.  65 

y.     If  1  bushel  of  corn  cost  7-3  cents,  what  will  '257  biislivl^ 
iuo  to  ? 

bifs/t,        r/S\  biLs//, 

If     1     :     75     ::     257 

75 

1^85  . 
1799 


192,75     Ans.  19'2  (ids.  75  cts. 

3.  Wlint  will  931  yards  cf  shalloon  conii?  to  at  55  cts.  4  ms. 
per  yard  ?  Ans.  515  dols.  77  els.  4  nis. 

4.  How  many  bushels  of  wheat  at  1  do!.    12  cts.  per  bushel 
can  I  have  for  81  dols.  76'  cts.  ?  Ans.  7o  bushcjs. 

5.  What  will  94  cwt.  of  iron  come  at  4  dols.  97  cts.  *2  rns. 
per  cvvt  ?  Ans.  467  diois.  SG  cts.  8  ms. 

o.   What  will  349  lbs.  of  beef  come  to  at  2,/.  per  lb.  ? 

.    An:^.   .C.2    18   2-^ 

7,    .\t  Cv.  per  \ard   wb.at  will  59  yards  of  cloth  come  to  ? 

Ans.  <£.S-  17  0 
I'rovc  this  answer  to  be  right.  . 

"^     ■  !  '^'.' many  lb-<.  of  beef  at  5  cts.   p^^^*  ^'      -  .: 

\^.  85  cts.  ? 

cAv.      lb.        (his.  cis\  . 
K  5    :     1   :  :     29,85 
I 


0^  How  many  hhds.  of  salt  at  4  .cols.  ^0  cl:f.  per  hlid.  ^c;-)) 
kfi\(*  ior  392  dols.  ?  .,  Aus.  hO  hln'i: 

'    .  How  many  lbs.  of  ccil\^c,  at  1^.  7^/.  rev  lb.  m:iy  ht-  \ 


F-2 


66  SINGLE  RULE  OF  TlJREt:  DIRECT. 

U.   Wlien  25  yds.  of  cloth  cost  £.2  V2  1,  what  is  it  per  yd.  ? 

ifL     £.  s.  (1.     ?/.7. 
If     25   :   2     12  1  ::  1 
20 

52 
12 

625 
1 

,e5)()25(12  I  25  • 

50  -^ 

2s,   hi, 

]  25 
125 

Air,.   2.?.    Id 

1?.  If  5o  bu?hels  of  corn  cost  42  dols.  56  cts.  what  is  it  per 
luihol?  bush.dolsA'tsbmh, 

If     5()  :  42,5ri  ::  L 
1 


5a)42,56"(,7(> 

336' 
336^ 


Ans.   7(^  ct«?. 


Kn   If  112  lbs.  o^  beef  cost  iS.5.  8 J.  wlmt  is  it 


])rr  ib. 


h.  } 


Ans.  2  pence. 
'73  l)iishcls  of  rye  cost  7o9  dols,  23  cts.  9  nis.  what 
^''-rtb  ?  Am.  1  (h)l.    14-  cts.  3  ids. 

1   vard    of  baize    wortli,    when    '^l    yards    cost 

..,,/.    '  Ans.  -^.  2^/. 

n  iioi)  is  sold  at  5  dols.  4  cts.  per  cv.t.  wh-u  i>  it  pv>r 

'^^     ,     \   rl:  .  5   :n-. 
'Ijns  of  mola;-  ^- .  '•  '^^1:;':  ^^^ 

Prove  t];is  :' 


SINGLE  RULE  OF  THREE  DIRECT.  €7 

ig.  At  5  dols.  50  cts.  per  thousand,  what  will  37  tliousand 
of  b*)ards  come  to  ?  Aiis.  '203  dols.  50  cts, 

20.  What  will  4  hhds.  of  rum  come  to,  containing  viz.  79j> 
81,  lOU,  and  112  gals,  at  6s.  9(L  per  gal.  ?     Ans.  £A'I7   4-  9 

:!.  Vv-hat  will  327  hhds.  of  salt  come  to,  at  5  d(ds.  25  cts. 
per  iihd.  ?  Ans.  17l6'  dols.  75  cts. 

C2.   If  3  and  4  make  9,  how  many  will  6  and  8  make  ? 

Ans.   18. 

23.  If  a  chest  of  Hyson  tea,  weighing  7^  lb.  neat,  cost 
£.32  I  U\  9^/.  what  is  it  per  lb.  ?  Ans.  Ss,  3d, 

24.  B  owes  £.21 19  17s.  6(1.  and  he  is  worth  but 
£'.1324  185.  old.;  if  he  delivers  this  to  his  creditors,  how 
much  do  tliey  receive  on  the  pound  ?  Ans.   12.s,  6V. 

2).  A  owes  B  £.069  6s.  8d.  but  failing  in  trade,  he  is  able 
to  pay  but  15^.  6d.  on  the  pound  ;  how  much  is  B  to  receive, 
and  what  is  his  loss  ?  Ans. — He  is  to  receive  £.441   4   8 

ITis  loss  is  ......  12s  2  0 

2o.  A  merchant  failing  in  trade,  owes  in  all  29475  dols.  and 

delivers  up  his  wdiole  propert}',  worth  2189-1'  dols.  3  cts.  ;  liow 

much   per  cent,  does  he  pay,  and  what  is  B*^s  loss,  to  whcMii  he 

owed  325  dols.  ?  Ans. — He  pays  74  dols.  28  cts.  per  cent. 

And  B  lo-es  S3  dols.  59  cts. 

27.   How  much  will  4  cwt.  1  qr.  19lb.  of  butler  come'  to,  v,% 


lb..? 

lb. 

400  n:  4  hundred. 
48  zz  excess,   12  per  cent: 

Ih 

^ 

28—1  quarter. 
19 

[f    1 

:     9      : 

:       495 

12)4455 


20)371     5 


Au-:.     £.18    \\s.  3d. 

SCib.  of  bice;  cobt  13  dols.   20  cts.    what  is  it 

Aiis.  12  cerits. 


63  SINGLE  RULE  OF  THREE  DIRECT; 

29.  If  \6  cwt.  3qrs.  of  steel  cost  157  dols.  45  cts.    vvliat  i>  ■ 
1  qr.  worth  ?  Ans.  2  dols.  35  cts. 

Prove  this  answer  to  be  right. 

30.  A  captain  of  a  ship  is  provided  with  1 8000  lb.  of  bread 
for  150  seamen,  of  winch  each  man  eats  4  lb.  per  week,  hffw 
long  will  it  last  them  ?  Ans.  30' wef^ks. 

31.  How  long  would  2295  lb.  of  beef  last  for  45  seamen,  if 
they  get  1  lb.  cach^  and  that  three  times  a  week  ? 

Ans.  17  weeks. 

32.  Suppose  120- seamen  are  provided  with  7200  gallons  of 
water  for  a  cruise  of  4  months,  each  montli  30  days;  how  much 
is  each  man^s  share  per  day  ?  Ans.  2  quarts. 

o3.     A  ship's  company  of  I6  men  is  on  an   aliowance   of  o 
ounces  of  bread  per  day,  when  meeting  with  a  vessel  from  winch 
they  are  supplied  with  2  cwt.  of  bread,    what  addition  will  this 
make  to  their  daily  allowance,  if  they  suppose  their  voyage    to  . 
last2S  days  ?  "       '  Ans.  8  ounces. 

34.  If  17  tuns  2  hlids.  of  wine  cost  54()3  dols.  40  cts.  h-'^v 
much  is  one  pint  worth  ?  Ans.  15  cts.  5  ms. 

35.  IkrvV  much  will  4  pieces  of  linen,  containing,  viz.   ooly  . 
36,  37  h,  and  3S  yards  come  to,  at  79  cts.  per  yarci  ? 

Ans.  110"  (hds.  13  ct?, 

36.  How  many  crov/ns  of  110  cts.  each  will  pay  a  debt  of  . 
£.  82  I6.S.  7(1  ?  "  An^.  251  vvo^^rv,^, 

37.  IfCOJ  tonspcwt.  3  qrs.  3lb.  oftallow  cost  £.433^^  3.0;/. 
what  does  1  ton  cost  ?  An?.  i;.22    8   i\ 

38.  I  low  many  cwt.  of  rice  may  be  bought  for  48/  dols.  50  cis. 
when  7  lb.  cost  25  cents  ?  Ans.  121  cwt.  3  (jr?.  14  lb. 

39.  \V!ieii  9  dols.  36  cts.  is  paid  for  2  ([rs.  22  ib.  of  sugar,  . 
wiiat  is  7  i-^.  w^orth  ?  Ans.  84  cts. 

40.  "When  47  cwt.  3qr5.  of  sugar  cost  ^£.182  Is.  llf/.  what  *. 
is  I  ([V.  worth  ?  Ans.  19-^.  I''/- 

-i  1        Ii"  n  t!).  6  oz..  xVvoirdupois  cost  5  dols.  JO  cts.  ^vi.  -r  i.  it  -. 

;\rs. 

.  ...      ..-;i..,;it 40  tubs  of  butter  wei-.v  '"  "   '  '  '^  '     '  ^ 

nC'ir,  i'oi'  -!v2  dols.  2  els.  ;  paid  coope;  .t 

and    labc-ur  4  d<ds.  S3  cts.  8    mills  ;   :■:'  .  :,    ->      . 
1  .would  know  wdial  it  stands- me  in  per  ;.>.  ?    /v..;;.  ;  i 


SIXGLE  RULE  OF  THREE  DIRECT.  69- 


4:3.     How  much  will  a  grindstone,  32  inches  iliiiinetcr,  luul  6 
inches  thick,  come  to,  at  5s,  per  cubictbot  ? 

Sec  iiedudwiiy  \  32     the  diameter. 


1 6  iz  liii i  1'  til c  d  i iiinc  tc  r. 


48 


If     l/i^S       :      5     ::      46'03  :  13    4       Ans.  13.?.  4?/.. 

4i.    Vv'hat  will  a  grindstone,  28  inches  diarnctfer,  and  3^  in-, 
chcs  thick,  come  to,  at  1  dol.  gOcts.  per  cubic  foot  ?  • 

Ans.  2  dels.  26  cts. 
45.     When  a  man's  yearly  income  is  2^9  dollars, Tfcw  much 
is  it  per  day  ?  Ans.  2  dols.  60  cts. 

46".     At  '^l  per  cent,  what  is  the  commission  en  1525  duls.  ? 

Ans.  6S  dols.  62  cts.  5  ms, 

47.  What  is  the  interest  of  456  dollars  for  1  year,  at  6  per 
cent.  ?  Ans.  27  dols.  36  cts. 

48.  At  5  dols.  50  cts.  per  Isl,  what  will  21,186  feet  boards 
come  to  ?  Ans.  1 16  dols.  52  cts.  3  uis. 

4p.    When  boards  arc  sold  at  IS  dols.  per  M.  what  is  it  per 
foot  ?  Ans.  1  cent  8  mills.' 

50.  What  will  93  feet  of  boards  come  to,  at  4  cts.  per  foot  ? 

Ans.  3  dols.  92  c-ts. 

5 1 .  What  will  45)  thousand  3  hundred  and  25  ca^ts  of  sIum s 
come  to  at  17  dols.  per  thousand  ? 

NoTK.     Stares  nre  cyuntcd  by  casUng  three  at  a  time  ;    40  ca^-ts   uvt*.ke  1' 
huiiUrtd,  iii\d  10  hundred  1  lhou;and. 


'^l. 

(^•.  's. 

3r. 

//. 

r. 

1        : 

17 

;;       49 

3 

26 

ro 

10 

i^. 

493 

40 

40 

dirJs-    Cts.  m, 
Ans.  8J9.  16    2 

400 

19745 

>0,     V/nat  will  19  M.  8  and  15  casts  of  white  oak  hhd,  staves 
iic  to,  at  31  dols.  per  M.  ?     Ans.  6l4  d^ols.  Q6  cts.  2  mk. 


?0  SINULK  l^ULK  or  UiRLK  l^U[V.C 


53.  What  will  Q2  M.  9  aiul  3?  ca'^t^  (;("  wd  o-ik  lilid.  f-.iA!ve5 
como  to,  at  1:)  dois.  ]:cr  M.  r        An-.  'JfyN;  (!ol>.  (]0(:{<.  QpAi. 

.5-k  \Mi:it  \\iil  .50"  bu:-uiiciot' iioops  come  to,  at  Qj  doli^.pcr 
M.  ot  30  bundles  ? 

NoTi-:.      ll:){)jis  ai\:   som^'/iriirs   K..nr.fl    iii  Ir.u'.dlcs  of  50  hoop- p:k-]),  ai;;!  1 
'^••'■^'  '■   -'''"-  ■■■■  '  1  hinir}:ed,  and   10  liui;d:-d  i-v  40  bund'e^,  1  ihuii-aiu!.   ]>i:t 
-\  b,ur,d  li!  l;ni;d'vv*  ol'di/ eaclij  o  b'.indics  iiiakinj;  1  liiUidrcd/, 
Ui.vj  I'^  iiu.i.li^.i  <jr  30  biuirl'e*^^  1  ihuusuiid, 
3).n) 
^;i//^.         ff:.K      ^-^-^^  Or   btinA.      r/*'/^.      ?';/;j/f. 

li'   iO     :     25  ::      3  ^i|  hundreds  00    :    25  : :  5f) 


25 


90 


2^0 
112 


5 10)  140(0 


4J,(;ui 


Ajis.  4G  dols.  6J  dimes,  or  6;^'  c;s. 

55.      How  many  bi-^diel^  (:(  i^alt,   at  4  dolb.  7  5  cts.  ]>ei'  hud, 
can  I  ba\c  ior  o'^ii  dollars  r 

1(4    73:    &    ::     o'26        An?.   5-1-9  biislieiN,  \\lieii  nioa^urcJ  on, 

board  tbo  vi^^-d. 
If  4   75  :   7^::     32u         An-.   5U  bu  '--'■■— ^    -'•,  —-'y, 


5^?.      W];at  i<  rlK    (a-  o-^  bo.d^,  ^  (-.  ^• 
ihc  d.;\vt  tax,  at  '2Sca  a:    -  .a  .;  .     '   ^  <  . 

57.      \V;;;'t  i~  {].'    1    -  '     •    ■  .    N  '■. 

the  dliS'Ct  t.ix,  at  /', 


lb  too     :     ,a      ::      fy' 0 


lbO)C7i',0 


nr     \-.     ^    n:i-  r>^i:I    is  rq';:d  to  3  nu'.h  on  u  .    > 


1;.'  u-i?  ^iiin  lu 


8     SINGLE  RULE  OF  TIirvEE  DIRECT.  71 

Examples. 

■58.      What  is  the  tax  on  7 bo  ctoil.iis  at  ,\  per  cent.  ? 
7.'^J  dollars 
3  mills 

'J',"*.">f)  ir.'.lis.  Ans.   2  rlols,  '25  cts.  9  ii'^"^* 

59.  Find  ll:c  t:ix  on  ihe  following  sums-  • 

<■/()>.  r/.;/.>.    r/,?. 

■vif'..    1 .);)(.)  at    ;',)  prr  cent.    An^.   ()  "^0 

4o00         1^   2^:  ^O 

7S50        ;^ 4  7  JO 

\'2(h^0         /, 8S  7() 

i()9.5()      ;■', ij.'>  Co 

2  !  M'20  ^'-'^ ••••••  V 0^1    5 1; 

:).' S  10  1     3.38  40 

60.  W  iiat  will  a  pierce  t^.f  land.  nucK-Lirinir  48  Ice:  i.':s  length 
and  4-0  kv\  \\\  widili  at  each  end,  amount  to  at  20  dolkub  per 
square  rod.?  fr^f^* 

48 
40 

/;,^        r/.,'.s.       

If  \17-ll  :  20  :  :    L920 

Piy  decimals.  ^  Ans.    Ill  dols.  4  ct?. 

If  272,2.3  :  20  ::  1^20 

61.  A  charter-party  for  a  ve?Hel  of  1  Si'T  tnns  commenced  on 
2$th  of  Ma^',  and  ended  on  tr.e  lOih  -f  (October  f'/ilowinL':  : 
AVlifit  does  the  hire  amoiuit  to  for  that  tiiiie,  Jit  2  <  ois.  per  ton 
per  niouili  of  30  days  ?  dcn^.s, 

I^T;=y 4 

J'iiui 3.) 

.1:.!/ .U 

A:-. II   i     ...     31 

2  do!s>.  ■[)er  mo.  Octf,»1)cr'  •  •  •   JO 

-II    JO         :  ;■"  J  :  :  1    -i 


in/3 

37 -i 


3,0)5059/ J 

'16BG40  An<'.     1636  (i'.)!s.  40c'J. 

Tn  c;;)ru^itino-  the  linu',  tli:^  d'lys  of  rcc-iving  and  tliicharnlj:^  the  vcssvl  :u« 
it>t;V  included. 


T'2  INVliPiSE   PROPORTION. 

INVERSE  FROPO RTION. 

"Whereas  m  the  Rule  of  Three  Direct,  more  requires 
more,  and  less  requires  iess,  in  this  rule  more  requires  less  and 
less  requires  more. 

Rule.  After  stating  the  terms  as  in  the  Rule  of  Three  Di- 
rect, multiply  the  iirit  and  second  terms  together,  and  divide 
the  product  by  the  third,  and  the  quotient  is  the  answer. 

Examples.  * 

1.  If  100  workmen  complete  apiece  of  work  in  12  days, 
how  many  are  suilicient  to  do  it  in  3  days  ? 

d.  m.  il. 

12     :      100  ::  3 
1'2 

3)1200 


400  Ans,  400  men. 

2.  If  8  boarders  drink  a  barrel  of  cyder  in  12  days  how  long 
woitld  it  last  if  4  more  came  among  them?  Ans.  8  days. 

3.  A  ship's  company  of  15  persons  is  supposed  to  have  biead 
to  last  their  voyage,  allowing  each  8  ounces  per  day — when 
tlicy  p;!ck  up  a  C]-cvv'  of  5  persons  in  distress,  to  whom  they  are 
wiliiTig  to  con.miinicate,  what  will  the  daily  allowance  of  each 
person  then  be  ?  Ans.  6  ounces. 

4  V.'hen  wlieat  is  sold  at  p3  cts.  per  bushel,  the  penny  loaf 
^veighs  12  ounces — what  must  it  weigh  when  the  v.  heat  is  1  dol, 
24  cts.  per  bushel  ?  Ans.  9  ounces. 

.5.  Ifov7  many  yards  of  baize,  3  qrs.  wide,  will  line  a  cloak, 
whirh  has  in  it  12  yds.  ofcamblet,  half  yard  v»ide?  Ans.  8  3^ds. 

('k  '■■•  no:^e  400  )^:cn  in  a  garri.  on  rre  ]^r»:vidcd  witl^  i.r(;\!- 
:  0   days,  hew    iiiany    iv.en  must   \v  -rnt   Cit,   ii   ihcy 

\.  \e  th(-  provisioi^s  last  60  .Irys  ?  Awv,.    iCO  n^cn. 

7.  AVI. at  sum  should  be  put  to  iidi'ic^st  to  p;;n  ns  much  in 
1  nionlh,  as  127doHarji  would  gain  in  12  uh  i  ;!;■•? 

A..>.    !,:- Idols. 


COMPOUND  PROPORTION.  73 

COMPOUND   PROPORTIOX, 

Compound  Propohtion  teaches  to  resolve  such  ({ucstions, 
ns  require  two  or  more  stalings  by  simple  proportion.       ,    ' 

Rule.  State  the  question,  by  placing  the  three  conditional 
terms  in  this  order:  that  which  is  the  principal  caus6"<Sf'g.iirt, 
loss,  or  action,  possesses  the  first  place;  that  which  den{Ues 
space  of  time  or  distance  of  place,  the  second  ;  and  that  which 
is  the  gain,  loss,  or  action  the  third  ;  then  place  the  other  two 
terms,  which  move  the  question,  un(kn'  those  of  the  same  name, 
ii'.id  if  the  blank  place  fall  under  the  third,  multiply  the  three 
last  terms  for  a  dividend,  and  the  two  iirst  for  a  divisor:  but  if 
the  blank  fall  under  the  first  or  second  place  multiply  the  first, 
second,  and  last  terms  together  for  a  dividend,  and  the  other 
two  for  a  divisor;  and  the  quotient  will  be  the  answer. 

Examples. 
1.     If£.100  in  12  months  gain  £.5,  how  much  will  £.400 
gain  in  3  months? 

£.  mo.       £, 

300     :      12   :  :   5 
400     :        3 


100      1.200 
12  5 


12|00)60iOO 

£'^  Ans.  £,5 

2.  If  8  men  make  24  rods  of  wall  in  6  days,  how  many  men 
will  build  18  rods  in  3  days? 


7)f.  (/.  r. 

S     :     6     :  :  .    24 

3      :  :      IS 

6 

24      108 
3  8 


72   ) 864(1 2 
72 

144 
144 
^  —  Ans.  12  men. 


74  COMPOUND  PROPORTION. 

3.  If  Jl  family  of  9  persons  spend  450  dollars  in  5  months^ 
how  much  woukl  be  sufficient  to  maintain  them  8  months,  if 
iivc  more  were  added  to  the  family  ?  Ans.    1 120  dols. 

4.  What  is  the  interest  of  ^\240  for  50  days,  at  5  per  cent, 
per  annum  ? 

£,  days,  £, 

100  :     36'5     :  :     5 

240  :        50 
50 


3  00      12000 
S65  5 


365|00)600|00(1      12   lOj 
36'5 

235 
20 


3^5)4700(12 
4380 


320 
12 


365)3840(10 


190 
4 


36'5)76"0(2 
730 

30  Ans.  £A   12   lOj 

N.  B.  Vij  omitting  to  multiply  hv  llic  rate  per  cent,  and  dividing  56.jOO 
by  it,  aro  foimd  tlic  fixed  divisors  of  7  JOO  for  .*>,  and  6003  for  0  per  cent,  pet 
auiumi  ^omc'in!'^-?  u.^cU  in  culculatijig  interest. 


COMPOUND  PROPORTION.  75 

6.  What  is  tlic  interest  of  65-^  dollars  for  iG-i  days,  at  6  per 
cent,  per  annum  ? 

100  654  dollars^ 

365  l6'-t 


6)36500  2616 

392'\ 

6083  the  fixed  divisor,  654 
fcund  as  above  directed. 


0083)  107-256(17,632 
6083 


46426 

42581 

38450 
30498 

19520 
18249 

12710 
12166 

544      Am,  I7d.  63c.  $m. 
^,     What  ia  the  iatcrcst  cf  947  dollars^  for  294  days,  at  5  per  cent,  [^i 
annum  ? 

947  dolls, 
294 

3788 
8523 
1-894 

yixed  Divisor     7300)278418(^30,13^^ 
21-900 

59418 
58400 


10180 
7300 


28800 
21900 


69000 
65700 


3.300  A»s.  oBduIs.  13  Q.  ^  la. 


76  VULGAll  FRACTIONS. 

VULGAK  TRACTIONS. 

Fii  ACTIONS,  or  broken  nuriilcrs,  are  expressions  for  any  as- 
sij,nable  parts  of  an  unit;  and  arc  represented  by  two  numbers, 
phited  one  above    the  other,  with  a  line  drawn    between  them. 

The  number  above  the  line  is  called  the  numerator.,  and  that 
below  the  line  the  denominator. 

The  denominator  shews  how  many  parts  the  integer  is  divid- 
ed into,  and  the  numerator  shews  how  many  of  those  parts  arc 
meant  by  the  fraction. 

Tractions  are  either  proper,  impropei,  compound,  or  mixed. 

1st.  A  proper  fraetion  is  when  the  numerator  is  less  than 
the  denominator,  as  J,  |,  f,^,  {J^,  &c. 

2d.  An  improper  j'raetion  is  when  tlie  numerator  is  either 
equal  to  or  greater  than  the  denominator,  as  f,  V^il'lu?  ^^» 

3(1.  A  eo?)? pound  fraction  is  a  fraction  of  fractions,  and 
knov.n  by  the  word  qf\  as  h  of  §,  y  of  /*q,  |§  ^^ ih  ^^' 

4th.  A  7nixcd  ninnler  or  fraction  is  composed  of  a  whole 
number  and  fraction,  as  8f,  izj,  29|,  &c. 

I.   To  reduce  a  simple  fraction  to  its  lowest  terms. 

Rule.  Find  a  common  measure  by  dividing  the  lower  term 
by  the  upper,  and  that  divisor  by  the  remainder,  continuing  till 
nothing  remains ;  the  last  divisor  is  the  common  measure;  then 
divide  both  parts  of  the  fraction  by  the  common  measure,  th'' 
quotients  express  the  fraction  required. 

NoTe.  If  the  common  measure  happens  to  be  i?  tjie  frac- 
tion is  already  in  its  lowest  term;  and  whcii  a  fraction  hath 
cyphers  at  the  right  hand,  it  may  be  abbreviated  by  cutting; 
them  off,  as  f  |2. 

Examples. 

1 .     Reduce  /,\  to  its  lowest  term. 
91)117(1 
91 


26)9l# 


Common  measure        13)2()(2 

2()  1  ^)^^i  (9  the  answer. 


TULGAR  FRACTIONS.  77 

Or,  divide  the  terms  of  the  fraction  by  any  number  that  will 
divide  them  without  a  remainder;  divide  the  quotients  in  the 
same  manner,  and  s6  on,  till  no  number  will  divide  them  both, 
and  the  last  quotients  express  the  fraction  in  its  lowest  terras- 

Examples. 

2.  Reduce  Hf  to  its  lowest  terms, 

W    W    C^) 
192    24      3     1 

zz — =z— n—  the  answer. 

576    72      9     3 

3.  Reduce  ^  t^  to  its  lowest  terms.  Ans.  f, 

4.  Reduce  ^^f  to  its  lowest  terms,  Ans.  |. 

5.  Reduce  |f ^f  to  its  lowest  terms.  Ans.  |-ij. 

II.  To  reduce  a  mixt  niDnber  to  an  improper  fraction. 

Rule.  Multiply  the  whole  numbers  by  the  denominator  of 
the  fraction,  and  to  the  product  add  the  numerator  for  a  new 
numerat^l^and  place  it  over  the  denominator. 

Note.     To  express  a  whole  uumbcr  fractiba-wise,  set  i,  fur  a  denominator 
to  the  given  number. 

'   "^'^  Examples. 

1.  Reduce^5g  to  an  improper  fraction. 

"*S><  a4-3=z^iji  the  answer. 

2.  Reduce  183 /j  to  An  improper  fraction.  Ans.  ^ff^. 

3.  Reduce  27f  to  an  iitiproper  fraction.  Ans.  ^|^. 

4.  Reduce  514  /^  to  an  improper  fraction.  Ans.  ^f|". 

^ 
III.  To  reduce  an  improper  fraction  to  its  proper  terms. 

Rule.  Divide  the  upper  term  by  the  low^r,  and  the  quo- 
lent  will  be  the  whole  number;  the  remainder,  if  any,  will  be 
■■'^  numerator  to  the  fractional  part.^j^ 

Examples. 

.     Reduce  ^J-  to  its  proper  terms, 
o)  1 7  (3  g  the  answer. 
15 


2.  Reduce  ' J^.to  its  proper  term*'.  Ans.  275. 

3.  Reduce  ^f  P  to  its  proper  terms,  Aus.  514/^- 

G2 


the 


?8  VULGAR  FRACTIONS. 

IV.   Tofind  the  hast  common  multiple  or  denominator. 

RuLF..  Divide  the  given  denominators  by  any  number  that 
uill  divide  two  or  more  of  them  without  a  remainder^  and  set 
llie  quotients  and  the  undivided  numbers  underneath.  Divide 
these  quotients  and  undivided  numbers  by  any  number  that  will 
cli\ide  two  or  more  of  them  as  before,  and  thus  continue,  till  no 
two  numbers  are  left  capable  of  being  lessened. 

Multiply  the  last  quotients  and  the  divisor  or  divisors  to- 
gether, and  the  product  will  be  the  least  common  denominator 
required.. 

Examples. 

1.     What  is  the  least  common  measure  of  |,^,  ^^,  &  ^(^  ? 
8)9     8     ]5     16' 

3)9     1      15       2 


3     1        5        2 

3x5x2=z30x3x8=z720  ans. 
2.  What  is  the  least  number  that  can  be  divided  by  the  nine 
digits  without  a  remainder?  Ans.  2520. 

V.  To  reduce  vulgar  fractions  to  a  common  denominator. 

Rule.  Find  a  common  denominator  by  the  last  case,  in 
wliich  divide  each  particular  denominator,  and  multiply  the 
quotient  by  its  own  numerator,  for  a  new  numerator,  and  the 
new  numerators,  being  placed  over  the  common  denominator, 
express  the  fractions  required  in  tlicir  lowest  terms. 

Examples. 

1.  Reduce  i,  |,  and  /^  to  a  common  denominator. 

36  the  com.  deuom. 

4  9x^-n 

9  4x5  —  ^20 

12  3x7=iV!l 

The  fractions  will  l^e  IJ,  |g,  fj. 

2.  Reduce  I,  f>.|,  and  I  to  a  common  denominator. 

/ins.  04,  04,  04,  ex  ^^. 
3^.     Reduce  I,  t,  ?  and  A  to  a  common  denominator,. 

-*,     Reduce  K  I,  A  and  J  to  a  common  denominator. 

"      ^       ^'  A,.S     J5      27      12     K,    25 


VULGAR  FRACTIONS.  79 

VI.  To  reduce  a  compound  JYaction  to  a  single  one. 

Rule.     Multiply  all  the  numerators  for  a  new  numerator,  • 
and  all  the  denominators  for  a  new  denominator,  then  reduoe 
the  new  fraction  to  its  lowest  term  by  Case  I, 

Examples. 

1.  Reduce  £  of  ^  of  ^.^  to  a  single  fraction. 

3x5x9—135     9, 

zz  ■     .'  the  answer. 
4x6x10  =  240   \6 

2.  Reduce  f  of  f  of  I J  to  a  single  fraction.     Ans.  //g. 

3.  Reduce  f  of  |  of  j  to  a  single  fraction.  Ans.t^Aj. 

VII.  To  reduce  a  fraction  of  one  denomination  to  the  fraction  of 

another,  but  greater,  retaining  the  same  ialue» 

Rule.  Reduce  the  given  fraction  to  a  compound  one,  by 
multiplying  it  with  all  the  denominations  between  it  and  that 
denomination,  to  which  you  would  reduce  it ;  then  reduce  that 
compound  fraction  to  a  single  one. 

Examples. 

1.  Reduce  g  of  a  penny  to  the  fraction  of  a  pound, 

d. 

7x1x1  7 

—   — zn— • the  answer. 

8X12X20   1920 

2.  Reduce  f  of  a  pennyweight  to  the  fraction  of  a  pound 
Troy.  Ans.  jJo- 

3.  Reduce  f-  of  a  pound  Avoirdupois  to  the  fraction  of  a- 
cwt.  x\ns.  ^Iq, 

VIII.  To  reduce  (he  fraction  of  one  denomination  to  the  fraction 

of  another,  but  less,   retaining  the  same  value. 

Rule.  Multiply  the  numerator  by  the  parts  contained  in 
the  several  denominations  between  k  and  that  denomination  to 
which  you  would  reduce  k  for  a  new  numerator,  and  place  it 
©ver  the  denominator  of  the  given  fraction. 

Examples. 

I.     Reduce  9^0  of  a  pound  to  the  fraction  of  a  penny. 
1X20X12  =  240 

=+  the  answer, 

9(yo 


so  VULGAR  FRACTIONS. 

2.  Reduce  s^q  of  a  lb.  troy  to  the  fraction  of  a  dwt.   Ans.f 

3.  Reduce  ^-Jg  of  a  cwt.  to  the  fraction  of  a  lb.  Ans.  | 

IX.  Tofnd  the  value  of  the  fraction  in  the  hioxcn  parts  of  the 

integer. 

Rule.  INIultiply  the  numerator  by  the  known  parts  of  the 
integer  and  divide  by  the  denominator. 

Examples. 

1.  What  is  the  value  of  f  of  a  £.  ? 

2 

20  shillings, 

3)40 

Ans.   13.?.  4</. 

2.  What  is  the  value  off  of  a  shilling  ?  A\\^Ad,Slqrs, 

3.  Reduce  f  of  a  lb.  troy  to  its  proper  quantity. 

Ans.  7oz.  4d\vt. 

4.  R^educe  |  of  a  mile  to  its  proper  quantity. 

Ans.  6  fur.  l6  poles. 

X.  To  reduce  any  given  quantity  to  the  fraction  of  a  greater  dc- 

nominatio?!  of  the  same  kind. 

Rule.  Reduce  the  given  quantity  to  the  lowest  denomina- 
tion mentioned  for  a  new  numerator,  under  which  set  the  in- 
tegral part  (reduced  to  the  same  name)  for  a  denominator,  and 
it  will  express  the  fraction  required. 

Examples. 

1.  Reduce  l6s,  Sd.  to  the  fraction  of  a  pound, 

16     8 
12 

200     5 

zz —  the  answer. 

240     6 

2.  Reduce  2  quarters  3  J-  nails  to  the  fraction  of  an  ell  Eng- 
lish. Ans.  ^^. 

3.  Reduce  4<y.  Old,  to  the  fraction  of  a  pound. 

A  im   J  ^  ^ 


AXILGAR  FRACTIONS.  SI 

ADDITION  OF  VULGAR  FRACTIONS. 

I.  To  add  fractions  that  have  a  common  denominator. 

Rule.     Add  their  numerators   together,  and  place  the  sum 
over  one  of  the  given  denominators. 

Examples. 

1.  Add  J,  f ,  I,  I,  and  |  together. 

1 
2 
4 
5 
7 

19 
— zr2^  the  answer 

2.  Add  ,^„  H-,  and  -K  together.  Ans.  l/^. 

3.  Add  J#   'io>  and  cfo  together.  Ans.  1J|. 
4]      AJa  i\^  II,  and  jf  together.                        Ans.  2^^. 

II.  To  ac^(/  W2f.rec?  numbers  'whose  fractions  hate  a  common  de- 
nominator, 

RuLi:.     Add  the  fractions  by  the  last  case^  and  the  integer 
as  in  whole  numbers. 

Examples. 
.     1 .     Add  2  A  ?  3  /i ,  4  ,\ ,  and  7  A  together. 

^1  1 
79 
'11 

37 A  answer. 

2.  Add  13A»  9i*  »  ^^^^  3/5  together.  Ans.  25j. 

3.  Add  1  ,\»  2  A*  3  A,  and  4ji  together.  Ans.  12. 

4.  Add  9  J  I,  7/4,  5  A,  and  8  {{  together.  Ans.  31?. 

III.   To  add  fractions   hating  diffcj^nt  denonwiafors. 

Rule.     Find    the  least  common  denominator  by  Case  III. 
•  n  Reductiun,  in  which  divide  each  denominator,  and  multiply 


82  VULGAR  FRACTIONS. 

the  quotient  by  its  numerator  ;  the  sum  of  the  products  is  « 
new  numerator  to  the  common  denominator,  and  the  fraction 
required. 

Examples. 

1.     Add  f,  I,  I,  2,  and  \i  together. 
24  com,  denom. 

3  8X    2  =  1^ 

4  6x  3  =  18 
6  4X  5  —  20 
8  3X    7=21 

12     2x11=22 

I J  =4-2-4  ^^^^  answer. 
5.     Aa^  |,  1   I,  1,  and  i  together.  Ans.  l.^^^o' 

3.     Add  f ,  I,  t,  L  -nd  ^5  together.  3^^. 

IV.  To  add  mixt  numbers  whose jru^A^rins  hate  different  denom'* 
inators» 

Rule.     Add  the  fractions  as  in  the  last  «ase,  and  c^^  x\\* 
tegers  as  in  whole  numbers. 

Examples, 

1.     Add  5f ,  61,  and  4J  together. 

24  com.  denomv 


H 

16 

H 

21 

H 

12 

ns. 

17/4 

45—9  1 

24  —  -^24 

2.  Add  If,  J  of  J,  and  9/0  together.  Ans.  llg-o- 

3.  Add  li^o»  6i»  I  of  J,  and  7^  together..       Ans.lC'//^- 

V.  JF/ie/i  the  fractions  are  af  several  denominations. 

Rule.  Reduce  them  to  their  proper  quantities  by  Case  IXm, 
in  Reduction,  and  add  as  before. 


VULGAR  FRACTIONS. 

Examples. 


S3 


i.  Acia  I  of  a  £,  to  ^%  of  a  shilling. 


s.     d. 
I  of  a  j^.~15     6f 

/o  of  a  *.  zz  0     85 


15  common  measure. 
10 
9 


Ans.      IT)   10r^3      tI  =  iA 

2.  Add  f  of  a  yard,  |  of  a  foot,  and  I  of  a  mile  together. 

Ans.  J  540yds.  2ft.  9  inches. 

3.  Add  J  of  a  week,  J  of  a  day,    and  ^  of  an  hour  together. 


SUBTRACTION  OF  lULGAR  FRACTIONS. 

J.  Tojind  the  difference  hetucen  s'mple fractions  that  hate  a  com* 
man  denomiiiator^ 

Rule.     Subtract  the  less  numerator  from  the  greater,  and 
under  the  remainder  put  the  denominator. 


From 
Take 

Rem. 


f 

f 

T 


Examples. 

21  i4. 

i  Z  It) 

13  10 

1 


i 


IT 
35 

J  3. 
3S 

4 
33 


m 


5 
209 


II.   To  subtract  a  fraction  or  mixt  nitmher  from  a  tjohole  m'mhcr* 

Rule.     Subtract  the  numerator  from  the  denominator,  and 
under  the  remainder  put  the  denominator,  and  carry  one  to  be 


deducted  from  the  integer. 

E 

"iAMPI.ES. 

From    3 

6 

10 

9 

100 

^       Take     0,\ 

.0/0 

99  ?.^ 

B       Ucm.    '2\l 

o.i. 

84,  VULGAR  FRACTIONS, 

III.  To  suhtrad  simple  fractions  that  have  no  common   clcnomi- 
nator. 

Rule.  By  Case  IV.  in  Reduction,  find  a  common  denom- 
inator, in  which  divide  each  denominator,  and  multiply  the 
quotient  by  its  numerator;  the  difference  between  the  products 
thus  found  is  a  numerator  to  the  common  denominator,  and  the 
answer  required. 


From  -J-}  take  /^. 


Examples. 
42  com.  dcnom. 


21 

2X17: 

=  34 

14 

.3X 

9- 

=27 

Rem. 

7    

4il  — 

■■l> 

tlie: 

answer* 

From 
Take 

i 

5 

.    HI 

Rem. 

1. 

i 

A 

1 

1^1 

In  ord»r  to  distinguish  the  greater  of  two  fractions,  let  them  be  reduced  to 
a  common  denominator,  as  in  case  V.  in  reduction  ;  and  that  fraction,  whose 
numerator  is  greater,  is  th.e  greater  i'r;iction;  the  ditlerejice  lictv/een  ihe  new 
numerators,  benig  set  over  the  common  dcnonnnator,  will  slicw  tljc  excess  or 
inequality. 

Example. 

Which  of  the  two  is  the  greater  fraction,  J  J  oi'IJ  •'* 
48  com.  denom. 

12     4X11=44 
16'     3xl5rz45 

Ans.  -J I  is  greater  by  ^q» 

iV.  To  subtract  a  fraction  or  mixt  mmihcr  from  a  mixt  nimilcr,, 
xvhcn  the  fractional  part  to  he  subtracted  is  greater  than  that 
from  which  it  is  to  he  subtracted. 

Rule.  Find  a  common  dcnomlnriior  and  a  now  numerator. 
Gs  in  the  last  case,    and    then   subtract   the   numerator  oi'  tl 
gj-cutcr  fraction  from  the  common  denominator,  and  to  tiie  \\ 


VULGAR  FRACTIONS. 


85 


m^inder  add  the  less  numerator,  and  set  the  sum  of  botTi  for  a 
new  numerator  over  the  common  denominator,  and  carry  one 
lo  the  integral  part,  and  proceed  as  in  whole  numbers. 


EXAIMPLES. 

27  common  denominator. 


From 
Take 


From     6} 
Take      0?^ 


li 


^^2  7 


3X1=3 
IX  Uzz:i-i 


Rem. 


10^ 
lA 

^60 


12^ 
6"^ 


^9^ 
0/. 


1  o  1  6  ••? 


V.  JFhcn  the  fractions  arc  of  different  denominations. 

Rule.     Reduce  them  to   their  proper  quantities  and  sub* 
tract  as  before. 

Examples. 

1.  From  \j  of  a£.  take  j\  of  a  shilling. 

15  common  denominator^ 


.?. 

d. 

— 

7)  of  a£.nl5 

^ 

lO 

,^0  of  a  5.1=  0 

3J 

9 

Rem.     15     3,^5 

2.  From  '^  of  a  £,  take  2  o^  a  shilling.  Ans.  14.s.  3(f, 

3.  From  5  of  a  lb.  troy  take  J  of  an  ounce. 

Ans.  80Z.  l6dwt.  l6grs. 

4.  From  7  weeks  take  Pi^^o  days.     Ans.  5w.  4d.  7h.  12m. 

5.  From  ^  of  a  yard  take  j  of  an  inch.     Ans.  5  inch.  Ibc. 


MULTIPLICATION  GF  VULGAR  FRACTIONS, 

li  :  LE.  Reduce  compound  fractions  to  simple  ones,  and  mixt 
nuni!  :ts  to  improper  fractions;  then  multiply  the  numerators 
top^ethL^r  for  a  new  numerator,  aud  the  denoniiuatori  for  a  nesv 
denominator. 

H 


S6  VrLGAR  FRACTIONS. 

Examples. 


3.     ^Mutlip]}^  4^  by  J. 


4i 


9X1 

2X8 


/^,  tlic  answer. 


'2.  Multiply  ^  by  ^.  Ans.  i^,. 

:].  Multiply  ■    !)y  ^.  Ans.  ^|. 

4.  I\lnlti])]y  4-:^|  by  ]3f.  Ans.  67-2 f^. 

5,  Mu!tij)ly  ^  off/ by  ^.  Ans.  5=L 
().  Multiply  /;,  by  ~  oi  g  of  f .  Ans.  ^. 


DIVISION  OF  VULGAR  FRACTIONS. 

PlULE.     Prejiaro  the  fractions  if  necessary;  then  invert  the 
divio^)r,  and  proceed  as  in  niuUiplicnlion. 

EXAMTLES. 

1.  Divide^  by  §: 

4X3 

zz  I ;  rz  ^'  the  answer, 

7X2 

2.  Divide  3j  by  9J. 

6  2 

19x2 

J/  -\^  Then /r!i  =:  J  the  answer. 

6X19 

3.  Divide  5  bv  Z^,.  Ans.  7-. 

4.  Divide  ,^  by  4^.  Ans.   !'. 

5.  •   Divide  (]l  by  J  of  7.  Ans.  i?'^ 

6.  Divide  5::Oj5  ly  ^  ofOI.  Ans.  7^^ 

MfS^'ELLANEOUS  QUESTIONS 

IN    THE    rUECE])IXG     RULES. 

1.  What  pprt  is  28]?.  of  33,\  ? 

2.  ^Vhat  will  remain   if  13 3  v.  and  7i^d,  be  t;;  .1  ? 

Ah..  JO.  IK'^V. 


VULGAR  FRACTIONS.  87 

3.  Wliich  is  tiie  greater  fraction,  ^^  or  /^  ? 

Ans.  ^-^5  is  greater  by  /% . 

4.  or  what  number  is  IjG  the  H  part  ?  Ans.  o68. 

5.  By  how  much  must  you  multiply  13f  that  the  product 


nui 


be  4^91  ?  A«^s.  3?. 


().  Find  two  numbers  so  that  .i|  of  the  one  will  be  as  much 
as  J^  of  the  other  ?  Ans.    1'26  &  208  or  63  <Sc  101-,  ^c. 

7,     Which  is  greater,  I  of  6"^.  or  l^.  QhL 

Ans.  is.  '2hd.  is  greater  by  ^^d. 

S.  A  lias  ^  of  3  of  a  ship,  and  Fi  §  off,  which  is  the  great- 
er bhare  and  by  how  much?      Ans.  A's  share  is  greater  by^. 

9.  A  farmer  being  ik^ked  how  many  sheep  he  had,  answer- 
ed, that  he  had  them  in  5  lieUis ;  in  the  lirst  he  had  |  of  his 
Hock,  in  the  second  -J,  in  the  third  -J,  in  the  fourth  ^^,  and  iu 
tiie  lifth  -1-30;     how  many  had  he  ?  Ans.  1200. 

RULE  OF  THREE  DIRECT  IN  VULGAR  FRACTIONS. 

Rule.  Having  stated  the  question,  make  the  necessary 
preparations,  as  in  Reduction  of  Fractions,  anil  invert  the  iirst 
term;  then  proceed  as  in  Multiplication  of  Fractions. 

Examples. 

1.  If  I  ofayard  of  cloth  cost,  J  ^^  ^  shilling,  v/liat  will  J 
«f  a  yard  come  to  ? 

yd.         .9.  nd. 

If   "I     :     f     : :   " i 
inverted 

4X2X7        s. 

iz  ;. ',*  =z  25.  itZ.  the  answer. 

1X3X8 

2.  If  i^^3  of  a  ship  cost  £,Q73  2s.  6d.  what  are  3^  of  her 
worth  ?  Ans.  ^'.227    12^.    \d, 

3.  If  ]  of  a  yard  cost  |  of  a  pound,  what  will  f  of  an  ell 
F.nglish  come  to  at  the  same  rate?  Ans.  £.2, 

^  4.     A  person  having  ^  of  a  coal  mine,  foUs  J  of  his  sliare  for 
£a71  :  what  is  the  whole  mine  valued  at  ?       Ans.  £.380* 


SS  VULGAR  FRACTIONS. 

Single  RuleofTIirce  inverse  in  Vulgar  Fractions. 

Examples. 

1.  If  C5f.9.  ^vill  pny  for  tlic  carriage  of  an  cwt.  145|  niilos^ 
kaw  far  may  6"^  cwt.  be  carried  lor  llie  same  money  ? 

Ans.  2'1^(^  miles. 

2.  If  ?j\  yls.  of  cloth  that  is  Ij  yard  wide,  be  sufhcient  to 
make  a  cioak,  how-*:  much  mast  I  have  of  that  sort,  which  is  | 
yard  witic,  to  make  another  oi  the  same  bigness  ?     Ans.  4j?  yd.s. 

3.  If  3,  nK-n  can  do  a  piece  of  work  in  4^  hours,  in  how 
mifeiiy  hours  will  10  men  do  the  same  work  ?  Ans.  ]  /<>,. 

4.  If  the  penny  whitc-h->af  weigh  7  oz.  when  a  l)ushel  of 
W;5cat  cost  5s.  6d.  what  is  the  bushel  w-orth  when  the  penny 
while-loaf  weighs  but  2  J  oz.  ^  Ans.  15^.  4^g?. 


FUACTICE 

I?  a  contraction  of  the  Rule  of  Three  direct,  when  the  first 
term  happens  to  be  an  unit,  or  one,  and  has  its  name  from  its 
frequent  use  in  business. 

THE  Ji ABLE. 


Parts  of  a  jt. 

,9.  d, 

10  is      I 

6    -8    A 

•^  I 

4'  I 

3     4    1 

2     6'    4 

2        A 

1      8    ^, 

I .^o 

Tarts  ot  a  shiliing. 
d. 

G      is       i 
4    i 

r.       1 

O       , .1 

11 A 

1  A 


i-'ailfc  ot  i 
Cxvt,  Qr. 
10 

5 

4 

2      2 

2 

1 


1 

1  0 


Parts  of  a  Cwt. 
Qrs.  lb. 


IG 

14 

8 

7 

4 

2 


"5 


Parts  ol  ^  Cwt. 

lb. 

28  is        i 

14      1 

8      i 

7     i 

^     /. 

H  A 

2      A 


Parts  of  I  Cwt. 

14  is      h 

7  1 

4  1 

Si  1 

9  1 

^  3  4 

1  ,J« 


PRACTTCE^  83' 

Case    I. 

U7ien  the  price  Is  an  aliquot,  or  eicn  part  of  a  s/nlli?ig. 

Rule.  Divide  the  given  number  by  the  part,  and  the  quo-- 
tient  is  the  answer  in  shillings;  what  remains  is  to  be  reduced^ 
as  in  Compound  Division. 

Examples. 
1.     What  will  4'596  yards  cos,t  at  6d»  per  yard? 


6V.     2 
2|0 


4596' 


lU      li 


Yards.  d. 

Q,     3746     at      4  per  yard. 

3.  1095 3    

4.  7596.. 

5.  3747  •• 
6\      3.03.. 


Ans.  £.114   18-?,- 

£.  s.  (]. 
Ans.  62  8  8 
13  13  9 

6*3  6  0 


■  1 15    12 


'U 


20      0     4.V 


Case  II. 

JVhcn  the  price  is  pence,  or  pence  and  fartliingSf  and  no  even  pari^ 
of  a  shilling. 

Rule.     Find  the  even  parts  for  the  price,  and  proceed  as  in^ 
Case  I,  and  the  sum  of  the  quotients  is  the  answer. 

E>tAMl>LES. 

1.     What  will  4937  yards  come  to,  at  9c/.  per  var  J  ? 
^      '      4937 


h 
i 

2IO 


246'8  6 
1234   3 

370I29 


Ans.  £aS^  2  9. 
II  2 


0^  PRACTICE. 

Yards,  fl. 

2.  e76\5     at        iSpcrvard.                    Ans. 

a.    ^G2 7  ..- 

4.  3159 7^-- 

5.  1496^ 11     

0\      1895 10^ 

7.  4-()89|    5^ 

8.  36'89 84 

*).      1871 2^ 

10.  8914 8| 

11.  a^ji^oh    9h . 

12.  9H    loj.-- ... 

13.  201i    ....    9 


£, 

5.. 

(T, 

92 

3 

4 

109 

14 

6' 

9cS 

14 

4.1 

()'8 

11 

4 

82 

IS 

1^7 

97 

13 

lU 

126 

15 

2^ 

19 

9 

9i 

306 

8 

41 

101 

9 

5| 

4 

3 

91 

7 

10 

Hi 

Case    III. 

JF/icn  the  price  is  shillings,  or  shillings  a?2d  pence,  and  an  €Te» 
p^rt  (if  a  pound. 

Rule.  Divide  the  given  quantity  by  the  even  part,  and  tlie- 
quotient  is  the  ansv;er  m  pounds.  If  there  be  a  remainder^ 
leduce  it  as  in  Compound  Division. 

Examples. 

1.     At  Cy.  Sc/.  per  yard,  what  will  473  yards  come  to? 
Gs.  8c/.  I  i  I  473 


Ans.^.i 57    135.  4f/. 

yards,  s,  d, 

2.  387          at  10                                An.?. 

3.  478     5  

4.  ?A)7     3  4 

5.  797^ 2  6'  

6.  1594- 1   8  


c£. 

s. 

d. 

^9o 

10 

0 

119 

10 

0 

66 

3 

4 

99 

13 

9 

13 

5 

5 

Case  IV. 

lllicn  the  price  is  shillings  or  shillings  and  pence,  tchich  males  n* 
even  part  of'  a  pound, 

ntTLE.  Find  the  even  parts  for  the  price,  and  divide  ns  in 
\ise  JU.  or  multiply  the  given  cfuantity  by  the  shillings,  and 
'ke  the  even  parts  of  shillings  for  the  penccj  as  in  Case  JL 


PRACTICE. 


91 


Examples. 
1.     What  cost  287  yards  at  I?*.  6d.  per  yard. 

First  method.  Second  method. 

287  287 

17  6 


10 
5 

'2   6 

^- 

143  10 
71  15 
.S5  17  6 

Ans. 

251/.  2s.  6d. 

2009 
287 
e I  i  I     143  6 


2 1 0)502 1 ^  6 
Abs.  251/.  2s.  6d. 


d. 


4. 

5. 

6. 

7. 

8. 

9. 
10. 
XI. 


f/ards.  s. 

"8172  at         15 

.S69i      19 

47G5     11  8     .. 

3718     18  4      .. 

709} 1 2  6      . . 

Sfl3      14  10     .. 

961   2  H   " 

158      5  Si   •' 

4705i 3  9      •- 

127      7  5|   .. 


.£.      S. 
Ans.  6129 
....    3506     9 

2779   11 

..••  3408  3 
....  443  5 
....  157  19 
....  13  9 
.  ..*.  45  5 
882     6 


d^. 


8 

4 

6 

41: 


47     9  lOi 


Case  V. 
7f7zc;^  the  price  is  an  even  number  of  shillings. 

Rule.  Multiply  the  quantity  by  half  the  shillings,  doub- 
ling the  first  (or  right  hand)  figure  of  the  product  for  shillings^ 
the  rest  are  pounds. 

Examples. 
1.  What  will  788  yards  come  to,  at  2  shillings  per  yard  ? 
788 

Izrhalf  the  shillings, 

Ans.    £.78  \6 


yards. 

2. 

347 

,n. 

638 

4. 

589J 

5, 

246 

6. 

su\ 

7. 

523 

8. 

745 

o. 

373^ 

10. 

270 

11. 

1721 

33. 

89;- 

5. 

4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
«4 


Ans.     69    8 
'    ...    191     8 

235  14 

1  ^^3     0 

....  194  17 
....  366  S 
..^.   .596     0 

3:^6     3 

'i70     0 

J  89   15 

...•.    1«7     2 


s^ 


PRACTICE. 


Case  VI. 

JF/ien  the  price  is  pounds^  slnllijigs,  Src. 

Rule.  INIultiply  the  integers  of  the  given  quantity  by  the 
pounds,  and  work  tor  the  shillinus,  &c.  by  such  ot"  the  preced- 
ing rules  as  you  think  best,  and  work  likewise  for  the  fraction- 
al parts  of  the  integer ;  the  sum  of  these  will  give  the  answer. 

Examples. 

1.  What  will  1/3  cwt.  1  qr.  14 lb.  of  sugar  come  to,  at 
£.3   155.  6c/.  per<rwt.  ? 

173      1-  14 
3    15     G 


s.  cl 
10 
5 


2 
1 
1  0 


1  qr. 
14  lb. 


519 
86   10 
43     5 
4     6     6 

0    18   10|- 
0     9     H 


Ans.   £.654     9     91 
cwt,  qrs.  lb. 


5. 


219  2    19 
310  3  22* 


at 


s.      il 

69  n 

53     8  ' 


£.     s.     d. 
Ans.  767   18     61 
834     7     5i 


In  working  quesiions  of  this  kind,    when  tlie  quantity  is  not  above  the  mul- 
lipiicanou  table,  ihe  follovviug  method  is  used. 

1.     What  will   45  cwt.  2  qrs.  14  lb.  of  sugar  come  to,  at, 
£.3  7  9  per  cwt.  ? 

3     7     9 


i6  18     9 
9 


152     8     9     price  of  45  cwt, 
2  qrf.   I        1    13   \0h  price  of  2  qrs. 
14  lb.     ^       0     8     bl  price  of  14  lb. 


Ans.  £.154   11      i 


PRACTICE.  93 

Tons.  ml.  qrs.  Ih.                            I.     s.  d.                          I.     s.     d. 

f.  57     2     8 3  17     9 223  16     2 

3.  19     3  13 2     5  10 45  10     6 

4.  75     3  25 48     5 183  18     4J 

5.  2      1    18 5.)     8 7     3  10 

6.  1     1    li 6o     9 4     5  Hi 

7.  0     3  19 54     0 2     9     7^ 

8.  37   14     2  14     hem;)              89     6  8     per  ton      3370  13     2 

9.  27   16     3   18 90  10       2520     0     5 

10.  15     2        92     5        71     9   lOi 

11.  17  10     2       9110        1603  10     9 


1.     What  will  37  cwt.  3  qrs.  7  lb.  of  su^ar  como  to,  at  14j 
•luls.  40  cts.  per  cwt.  ? 


14,40 
37 


544,50  Ans.  544flols.  50  etf . 

r.>?is.  cwt.  q-r.  Ih.  (lols.  cis.  doh.  cts, 

2.  24  18     3  18  of  hemp  at         289  50  per  ton.     Am.  7921  73 

3.  31     iO  ' 268  75 8546  25 

4.  19  14     2  12  iron 110         2170  33  8 

5.  17     3  24  cordage    ••••      14        per  cwt.     •••.      251   50 
J.  R.per.  diyls.  cts.  doh.  cts, 

6.  25  2  25  of  land  at  29  per  acre.         Ans.  744     3 

7.  87   137 33  2886  88 

8.  229  3  18 18  50  4252  45| 

9.  3  26 »  •  •  25     22  81 


1.     How  much  will. 4-9  M.  3  hund.  25  casts  of  staves  come 
to,  at  17  dols.  per  M.  .? 


49 

17 

343 

49 
2  Ijund.         I  .'3,4 

1  i  1,7 

"20  casts  i  ,85 

5  i  ,212 


839,162  Ans.  859  dols.  16  cts.  2m. 


94.  PRACTICE. 

M.  hun.  caf^ts.  chls.       -  dnh.  cfs. 

2.  19     8      15  W.O.  hhtl.  staves  :>]  per  BL  Ans.  614  96 

3.  22     9     o7  II.  O.   do.     do.  13 298  90 

4.  28     1,      8  W.O.  barrel  do.  16 449  92 

5.  4     2     11 15.. 63  41 


1.  What  will  8,7^7  feet  of  merchantable  boards  come  to^ 
at  3Sa'.  6W.  per  M.  ? 

8,767 
38  6 

70135  . 
26*301 
6iL     I  4383 

20)337,529  shillings* 

Ans,  £.16  17  6 

The  fourth  figure  of  the  product  of  the  remainder,  multipli- 
ed by  12,  is  set  down  for  pence. 

s,  d,  £,    s.    d. 

2.  IS, 370  (t,  mcr. boards     39  8  per  M.      Ans.  36     8     8 

3.  2,819  do.  do.    -do.         37  4* 5      5      2 

4.  ,327  do.  do.,    do.  410 0   13      5 

5.  ,lh:>do.reiusedo.         20  6 ...»    0     3     9 

What  is  the  amount  of  a  seaman's  wages  from  the  loth  of 
!March  to  the  6th  ot  December  following,   being  8  months  and 
20  tlays,  at  l6  dollars  per  month  ? 
16 
8 

128  for  8  months. 
15  davs       8 
5  2,66| 

138,66f  Ans.  138  dols^.  66-,  cts. 

Note.     Iu  calculating  the  time  of  seaman's  service,   cither  of  the  dajs  of 
en^aning  or  beiiiL;  disclsargcd  is  taken,  but  not  both. 

What  is  the  amount  of  a  seaman's  wages  from  15th  of  JiuJ| 
to  the  28th  of  May  tbllovving,  at  15  dols.  per  month  .?  ^ 

Ans.   171  dols. 


PRACTICE.  9^ 

At  £A  11   3  per  cwt.  what  will  3  qrs.  25 J  lb.  come  to? 
£.4   113  # 


oqrs.  h         ^     ^  7h 

1  qr.  i           1      2  ^1 

3  4^  lb.  J          0   11  45 

7  ^05  8^6 

3^.  h          0      2  lOy^. 

r  I          0     0  9ni2 

Ans.  £.4     9     2-Jil 

AVhat  will  19  tons,    19cwt.  3qrs.  27^lb.   come  to,  at  £.19 
,)95\  ii5u.  per  ion  ? 

"*  Aks.  £.399  19^.  HHU- 


TARE  AND  TRET. 

Taue  and  Thet  are  allowances  made  in  selling  goods  by 
weight. 

Tare  is  an  allowance  made  to  thcbu\^cr  for  thcwei^br  of  rhe 
hogshead,  bavrcd,  or  bag,  containing  the  c;)nii:;odiry. 

Tret  is  an  allowance  for  waste,  dust,  is.c.  generally  at  4-  lb. 
per  1041b. 

Cloff'ia  an  allowance  for  the  turn  of  the  scale,  at  2  lb.  per 
3  cwt. 

Gross  weiulit  is  tlie  >ibt  o(  the  goods,  togctlier  with 

the  hogshead,  l-arrel,  oi'  luls  <^^c.  that  contains  them. 

Sutt/e  is  wlicn  part  of  the  allowance  is  lieducted  from  tlic 
gross. 

Neai  weight  is  what  remains  after  all  allowances  arc  made. 


S6 


TARE  AND  TllET. 


Citstom 'house  alloxcanccs 

Tare  on  whole  chests  of  lb. 

bohea   tea   ........  70 

•  ••  •on  every  half  chestdo.  S6 

•  •  •  •  on  quarter  do,  20 

•  •  •  •  on  every  chest  of  h}-^ 

son,  or  other  green 
teas,  the  gross  wt.  of 
which  is  70lb.  or  up- 
wards      20 

•  •  •  •  on  every  box  of  other 

tea,  not  less  than  50 
lb.  or  more  than  70 

lb.  gross 18 

If  801b.  gross 20 

And  from  SO  lb.  gross  and 

upwards •    •  •    22 


on  tea,  coffee,  and  svgar. 

Which  tare  shall  include  rope, 
canvas,  and  other  cover* 
ings. 

Tare  for  all  other  boxes  of  tea, 
according  to  invoice,  or  act- 
ual weight  thereof. 

Tare  for  coffee  in  bags  2  per  100 
.  • . .  •...•.  in  bales  S     do. 

in  casks  12     do. 

Oh  sugar,  other  than  loaf — ■ 

•  •  •in casks  12  ^o. 

in  boxes]  5    do. 

....  ......  in  bags 

or  mats  5    do. 


There  is  an  allowance  of  two  per  cent,  for  leakage  on  the  quantity  which 
shall  appear  to  be  contained  in  anj  cask  of  lirfuor  subject  to  duty  by  the  gal- 
lon ;  and  ten  per  cent,  on  all  beer^  ale,  arid  porter  in  boUles,  and  5  per  cent, 
on  all  other  liquors  in  bottles  in  lieu  of  breakage,  or  the  duties  may  be  com- 
puted on  the  actual  quantity,  at  the  option  of  the  im])ortcr,  to  be  made  at  the 
time  of  cntnj. 

Examples. 

1.  Sold  ten  casks  of  allum,  weighing  gross  33  cw^t.  2  qrs. 
15  lb.  tare  15  lb.  peroask  ;  what  is  the  amount  at  23^.  4c/.  per 
cwt. .? 

cxvt,  qr.    //;. 
gross     33     2     15  10  casks, 

tare         1      1      10  15  lb.  per  cask. 


neat      32     1 


112)150 


C.l    1   10  tare. 
Ans.  £.37   13  6^ 

2.     At  1  dol.  25  cts.  per  lb.  what  will  3  chests  of  hyson  tea 

come  to,   weighing  gr;.Sb  96  lb.  97l'o.   and  101  ib.  ;  tare  CC- lb. 
per  chest  >  ^   ^  Ans.   2^2  dois.  50  cts. 


TARE  AND  THET.  f)r 

3.  At  9  dols.  49  cts.  per  cwt.  what  will  3  lihds.  of  tobacco 
come  to,  weighing  gross,  viz. 

cwt.  qrs.  lb.  lb. 

No.  1.                 9     3     '25^  tare  149 

2.  10     2     12  ioO 

3.  11     1     25  158 

Ans.  265  dols.  46J-  cents. 

4.  At  79'^.  9^^*  p<?i*  cwt.  how  much  will  4  hhds.  oi"  madder 
come  to,  weighing  gross,  viz. 

cut.  qrs.  lb. 
]S^o.  1.  10     3     'i 

2.  11     2  13 

3.  10     1   16 

4.  14     3  19  tare  14  lb.  per  cwt. 

111b.    I  I  47     2  24  gross 
■^  5      3  24  tare 


413    0  neat. 

Ans.  £.1^6  9  6^, 

5.  At  6%s,  per  cwt.    what  will   a  hhd.   of  sugar  come  to, 
weighing  gross  7  cwt.  1  qr. ;  tare  12  lb. percwt. .?  Ans. .£.20   1   4. 

6,  At  21  cents  per  lb.   what  will  6  hhds.  of  cotlee  come  to, 
weighing  gross,  viz. 

No. 


rwf. 

qn. 

.  /6. 

Uu 

1. 

7 

1 

14 

tare  96 

2. 

8 

2 

21 

98 

3. 

7 

1 

21 

91 

4. 

6 

3 

25 

90 

.5. 

7 

0 

23 

89 

6. 

8 

1 

12 

Ans. 

100 
964  dols.  32  cent?. 

7.  What  would  the  above  cofiec  amount  to,  allowing  12  lb. 
per  cwt.  as  tare  on  the  gross   weight?     Ans.    96'tidols.  84  cts. 

8.  At  725»  6V/.  percwt.  how  much  will  8  hhds.  of  sugar  come 
to,  weighing  gross  each  8  cwt.  3  qrs.  7  lb.;  tare  12lb.  per  cwt.? 

Ans.  £.228  3  7|. 

9.  At  23  cents  per  lb.    what  will  4  bags  of  cotFee  come  to, 
weighing  gross  450  lb.  ;  tare  2  per  cent,  or  2  lb.  per  100  lb.  ? 

Ans.    101  dols.  43  cents. 

10.  At  12dolSk  50  cents  per  cwt.  what  will  3  barrels  of  su- 
gar come  to,  weighing  gross,  viz. 

cwt.  qrs.   lb. 
No.   1.  2     2     10 

2.  2     1     21 

3.  2     0     15  Tare  21  lb.  pr>r  barrel. 

Ans*  82  dols.  47  cts.  7  iti, 
I 


[^  TARE  AND  TRET. 

11.  At  15  dols.  40cts.  per  cwt.  what  will  4  hhds.  of  sugar 
CODie  to,  weighing  gross,  viz. 

cwt.  qrs.   lb. 
Ko.   1.  7     S      lo 

2.  8      1      10 

3.  7     2     12 

4.  8     1     21  Tare  12 ]b.  per  cwt. 

Ans.  443-doIs.  45  cts.  7  ms. 

1^2.  A  has  in  his  possession  a  hluh  of  sugar,  weighing  gross 
9  cwt.  3  qrs.  owned  equally  between  him  and  B.  It  is  required 
to  know  how  much  sugar  he  should  weigh  out  to  B,  allowing 
tare  12  lb.  per  cwt.  ?  Ans.  4  cwt.  1  qr.  1  U  lb. 

13.  At  191  cents  per  lb.  what  will  2  hhds.  of  coffee  come 
to,  weighing  gross  1 5  cwt.  3  qrs.  11  lb.  allowing  cuslom-htuse 
tare  or"l2  lb.  per  100  ?  ^ 

15      3    11 


1500  zn  filleen  Inmrlrcd. 
180  zz  15x  5  2  for  excess  in  each  cwt. 
81  zz  three  quarters. 
11 

1775 
Tare  1 2  per  100. 


Gross 
Tare 

Neat 

1775 

213 

1562 
19X 

11058 
1562 
781 

S0159  cts. 

213,00. 


Ans.  301  dols.  59  ds. 

14.  B  buys  of  C  a  hogshead  of  Coffee,  weighing  gross  9  cwt. 
2  qrs.  tare  12  lb.  per  cwt.  what  will  it  amount  to  at  23  cents 
per  lb.  ?  Ans.  218  dols.  50  cents. 

15.  If  custom-house  tare,  or  12  lb.  per  100,  were  allowed 
on  the  above  coffee,  what  would  it  amount  to,  and  what  differ- 
ence would  it  make  to  th.e  buyer  ? 

Aiis.  It  amounts  lo  ^15  dols.  51  cts.  being  2  dols.  99  ct3.  hi  his  favour. 

16.  What  is  the  gross  weight  of  a  hogshead  of  tobacco, 
weighing  neat  11  cwt.  1  qr.  tare  14 lb.  per  c^vt.  ? 

Ans.  12  cwt.  3qr.-.  12  lb. 


SINGLE  FELLOWSHIP.  99 

FELLOJVSHIP 

Is  wlien  two  or  more  join  their  stocks  and  trade  together, 
dividin*.';  their  g;iin  or  loss,  in  proportion  to  each  perbon's  bliaie 
in  the  joint  stock, 

SINGLE  FELLOWSHIP. 

m 

Single  Fellowship  is  when  different  stocks  are  employed  for  a 
certain  equal  time. 

Rule.  As  the  whole  stock  is  to  the  whole  gain  or  loss,  so 
is  each  man's  particular  stock  to  ixis  particular  share  of  the 
«jain  or  loss. 

Examples. 

1.*  A  and  B  buy  certain  merchandizes,  amounting  to  £.120, 
of  which  A  pays  £.80  and  B  £.4-0,  and  they  gain  by  them 
£.32 — what  part  of  it  belongs  to  each  ? 

A  £.80 

B      40 

As7^-32--   I  ^^     Ans.£.21     6     8  A. 

2.  A  ship  worth  8400  dollars  being  lost  at  sea,  of  which  J 
belonged  to  A,  J  to  B,  and  the  remainder  to  C,  what  loss  will 
each  sustain,  supposing  they  have  OOOO  dollars  insured  ? 

Ans.  A's  loss  6'00,  B's  800,  and  C's  TOOO  dols. 

3.  A  and  B  have  gained  1260  dollars,  whereof  A  is  to  hav« 
10  per  cent,  more  than  B,  what  is  the  share  of  each  ? 

Ans.  A's  66Q),  B*s  Goo  dols. 

4.  A  bankrupt  is  indebted  to  A  500  dols.  37  cts,  to  B  228 
dols.  to  C  1291  dols.  23  cts.  to  D  709  dols.  4-0  cts.  and  his  es- 
tate is  worth  but  2046  dols.  75  cts.  how  much  does  he  pay  per 
vent,  and  what  is  each  creditor  to  receive  ? 

Ans.  He  pays  75  per  cent,  and  A's  part  is  375  dols.  27^1  cts. 
B's  171  dols.  C's  968  dols.  42^  cts.  and  D's  532  dols.  5  cts. 

5.  Three  boys,  John,  James  and  William,  buy  a  tottery 
ticket  for  3  dols.  of  which  John  pays  tjO  cts.  James  1  dol.  and 
William  the  remainder.  This  ticket  is  entitled  to  a  prize  of 
2000  dollars,  subject  to  a  deduction  of  123  percent,  how  much 
is  each  to  receive  } 

Ans.  John  o25  dols.  James  5^3  dols.  333  cts.  William  64.1^ 
do  Is.  661  cts.. 


ICO  DOUBLE  FELLOWSHIP. 

6.  Tlirce  merchants  made  a  joint  stock — A  put  in  £.565 
6  8,  B  .£.478  5  4,  and  G  a  certain  sum,  and  they  :gaincd 
£.373  9  11,  of  which  C  took  for  his  part  £.112  11  11 — re- 
quired A  and  B's  part  of  the  gain,  and  how  much  C  put  in? 

Ans.  A's  gain  £.141  6  8,  B's£.119  11  4,  and  C  put  in 
£A50  7   8. 

7.  Three  men  have  to  share  a  legacy  of  1500dols.  of  which 
B  is  to  have  |,  C  |  and  D  the  remainder,  but  C  relinquishes 
his  part  to  B  and  D,  leaving  it  to  be  divided  between  them, ac- 
cording to  their  shares  in  the  whole.  It  is  required  to  know 
bow  much  of  the  legacy  B  and  D  receive  respectively  ? 

Ans.  B's  part  u  1000,  D's  500  dols. 


DOUBLE  FELLOWSHIF. 

Double  Fellowship  is  when  the  stocks  are  emplo^'ed  for  dif- 
ferent times. 

Rule.  Multiply  each  man's  stock  by  its  time,  and  add  them 
together,  then  say,  As  the  sum  of  the  products  is  to  the  whole 
gain  or  loss,  so  is  the  product  of  each  man's  stock  and  time  to 
his  share  of  the  gain  or  loss. 

Examples. 

1.  Band  C  trade  in  company,  B  put  in  .£.950  for  5  months, 
and  C  £.785  for  6 months,  and  by  trading  they  gain  £.275  18 
4  ;  wdiat  is  each  man's  part  of  the  profit  ? 

B's  fctock  930x5=:4750 

C's  7o5x6=r47lO 

A   TTHT.     o'y-^o  A         ^  4750  :  M38  10  10  B's. 
As  9400  :  27o   18  4  :  :     I  ^..^       ^..-,     r,     r  f*> 
(  4/10  ;     lo7     7     0  Ls. 

2.  Two  merchants  enter  into  partncrshF}>  for  l6  months.  A 
put  into  stock  at  first  1200  dols.  and  at  the  end  of  9  months 
*200  dols.  more,  B  put  in  at  first  1500  dols.  and  at  the  expira- 
tion of  6  months  took  out  500  dols. — w  ith  this  stock  they  gain- 
ed 7/2  dols,  20  els.  what  is  each  man's  part  of  it  } 

Ans.  A's  401  dols.  70  cts. — B's  ^370  dols.  50  cts. 

3.  Two  pcrsoris  hired  a  coach  in  Boston,  to  go  40  miles,  for 
20  dols.  with  liberty  to  take  in  2  more  when  they  pleased. 
Now  when  they  had  gone  15  miles,  they  admit  C,  who  wished 
to  go  the  same  route,  and  on  their  return,  within  25  miles  of 
Jloston,  they  admit  D  fur  the  remainder  of  the  journey.  Now 
j»s  each  pers-on  is  to  pay  in  proportion  to  the  distance  he  rode, 
it  is  required  to  settle  the  coach-hire  between  them. 

Ans.  A  and  B  6  dols.  40  cts.  each,  C  5  dols.  20  cts.  and  D  $  dois. 


SmrLE  INTEREST.  lOi 

SIMPLE  INTEREST 

h  a  compensation  made  by  Hie  borrower  of  any  sum  of  mo- 
nc}^  to  the  lender,  according  to  a  certain  rate  per  cent,  agreed 
on  for  the  principal  only. 

The  legal  rate  of  interest  in  Massachusetts  is  6  per  cent. 
Principaly  is  the  money  lent. 
Bate,  is  the  sum  per  cent,  agreed  on. 
Amount,  is  the  principal  and  interest  added  together. 
General  Rule.  '  Multiply  the   principal   by  the  rate  per 
cent,  and  divide  the  product  by  100,  and  the   quotient  is  the' 
answer  for  one  year. 

Examples. 

I.  What  is  the  interest  of  ^,496  for  one  year  at  6  per  cent*  ?' 

496 

d 

29|76 
20 

lo|20 

i>|40 
4 

1|60  Ans.  29/.  15s.  ^d: 

2.  What  is  the  interest  of  £.383   15  9  for  2  years',  at  Sj  per 
cent.  ? 

383  15    9: 


3070- 

6 

0 

191 

17 

lOf 

32|62 

3  lOi. 

ao 

12|43 

b\$6 
4 

sn. 

125. 

5^. 

for 

ono 

1|06 

yea?;-' 

S{ 

I  2 


Ans.     66    4    lO-Jfor  2  ye^rv- 


3  02  SIMPLE  INTEREST. 

3.  What  will  ^.826  13  9  amount  to  in  1  year  at  5  per  cent.  ? 

3zi:./y)826   ]3  9     principal. 
41     6  8i   interest. 

Ans.  <£.868      0  5l    amount. 

4.  "What  is  the  interest  of   ^.103   114,  for  4  years,  at  7  J 
percent,  per  annum  ?  Ans.  ^£.31    1   4r;. 

5.  What  will  £36  14  9    amount  to,    in  3  years,    at  5  per 
cent,  per  annum?  Ans.  ^€.42  4   ll|. 

6.  What  is  the  amount  of  .£19   15  8,  for  5  years,  at  6'|  per 
cent,  per  annum  ?  Ans.  £,26  9  U- 

7.  How  much  is  the  interest  of  £.72  12  6,  for  6'  months,  at 
C  per  cent,  per  annum  ? 

72  12     6 
6 


4 1 35  15     0 
20 


7jl5 
12 

1180  /.     s.     d. 

4  t)m,|;)4     7      J  J  for  one  year. 


3|20  ;  Ans.  2     3      6^  for  6  inontlis. 

Note.  Wlien  tlie  time  is  monllis,  mulliplying  by  the  rate  for  tlie  time 
gwes  the  answer.  This  rate  is  found  by  multiplexing  the  time  b}?  the  given- 
rate  per  cent,  for  a  year,  and  dividing  the  product  by  12.  The  quotient  is 
the  rate  required,  and  is  always  equal  to  half  the  months  when  the  yearly 
late  is  6  per  cent. 

8.  What  is  the  interest  of  £.25   19  3  for  8  months,  at  6  per 
cent.  j>er  annum  ? 

8  monthsi  25     19     3 

6  4 


12)48  1,03     17 

—  20 

4  rate  ~  half  the  months.      

0,77 
12 

9,24 


Aas.  £.  i  0  £>. 


SIMPLE  INTEREST.  103 

9.  IIow  much  will  £,5S  9  4  amount  to,  in  20  months,  at 
G  per  cent,  per  annum  ?  Ans.  £5S   16  3.. 

10.  How  much   is  the  interest  on  a  bond  of  £.2g5   IJ  10- 

for  18  months,  at  8  per  cent,  per  annum  ? 

j8  295    17     10 

g  1 2  the  rate  for  the  time*. 


12)144  35,50     14     0 

20 

12  

10,14  * 

12 

1,68 
4 

2,72  AOS.-35/.  10s.  Ifd. 

11-  How  much  is  the  interest  of  ,£80  12  9,  for  23  months^ 
at  6  per  cent,  per  annum  ?  Ans.  £,9  5  5j. 

12.  How  much  is  the  interest  of  £.36  14"  9  froni  I9th  May 
to  25th  October,  at  6  percent.  ?  '^ 

36  14     9  4ni.— 1)2     4     1  fgr  1  year. 


0  14     8i 
1  m.rzi  0     3     8 
6  d.—i  0     0     8|; 

2,20     8     6 
20 

4,08  Ans.    0  19     1 

12 

1,02 

13.  What  will  £.187  14  9  amount  to,  from  11th  June, 
1797,  to  26ih  October,  1798,  at  6*  per  cent,  per  annum  ?  ' 

Ans.  £.203  4  5j. 

14.  How  much  is  the  interest  of  £.19  13  7  from  3d.  Janua- 
ry, 1797,  to  18th  May,  1798,  at  6'  per  cent,  per  annum  ? 

Ans.  £.1    12  54. 

Tojind  the  interest  of  any  sum  for  months,  at  6  per  cent,  per  an^ 
num,  by  contraction, 

lluLE.  INIultiply  the  pounds  by  the  number  of  months  ;  the 
first  or  units  figure  of  the  product  is  pence,  and  the  rest  are 
shillings,  observing  to  increase  the  pence  in  the  prod^uct  by  1 

'  «^ii  they  exceed  4. 


104  SIMPLE  inteuest: 


Examples. 


15.  What  is  the  interest  o^  £.56  for  1,  5,  7?  and  12  monthsr 
56  56  56  56 

mo.  1  5  7  12 


All's.  5s.  7<i. 

28s.  0^. 

39s.  2d. 

67s.  2d. 

16.  £.  45 

17.  324 

18.  19 

19.  11 

for      6 
5 
7 
1 

months. 

Ans.l     7 
8     2 
0   13 
0      1 

0 
0 
3 

1 

If  there  are  shillings,  S^c, 

To  the  pounds  add  the  decimal  of  the  nearest  even  number 
of  shillings  (this  will  be  sufiiciently  exact  for  business)  and  mul- 
tiply by  the  months  as  betore,  separate  two  figures  of  the  pro- 
duct to  the  right,  and  the  left  hand  figures  are  the  shillings^ 
then  multiply  the  figures  pointed  off,  by  12,  and  the  product, 
rejecting  two  figures  to  the  right,  is  the  pence  of  the  answer. 

2 
,1 

20.  How  much  is  the  interest  of  £.347  5  9  for  3  months  ? 
347,3 
3 

shillings     104,19 


4 

6 

8 

10 

12 

14 

16 

18   shillinejs. 

/i- 

,3 

,4 

A 

>6 

,r 

,8 

,9  decimals. 

Ans.     51.  4s.  2d. 

21.  How  much  is  the  interest  of  £.195  15  lOj  for  10  months? 

195,8 

10  ,80 

12 

shillings     195,80  

Ans.  9/.  Ids.  9id.  4 

2,40 

The  value  of  the  remainder  is  thus  shewn  to  be  9ld. 


SIMPLE  INTEREST.  105 

22.    What  is  the  interest  of  £.590  19  9£    for  3    years,  7 
months  and  19  days  ? 

£.591   nearly. 
43 


1773 
2364 
15  days  i    295 
3  i       59 

1         i     19 


2578,6 -f  1  because  it  exceeds  4— see  the  Ruk. 


£.128  18  7 


23.  How  much  is  the  interest  of  £.476  9  8  for  9  montks 
and  13  <Jays  ? 

476,5 
9 

4288,5 

10  days  J     158,8 

3  do.  ^        47,6 

449,49 

Ans.  £.22  9  55 

24.  What  is  the  interest  of  £.40  for  7  yews,  5  months,  and 
2-6  days  ? 

40 

89  months. 


3.560 
15  days  J  20 

10  do.   i  13 

1  do.    1^0  1 

359,4 
Ans.  £.17  195 


106  SIMPLE  INTEREST. 

25.  What  is  the  interest  of  £.240  for  50  (hiys,  at()  per  cent.? 

Or  by  Comjiuund  l*roporlioa, 
240  i240 

6  50 


UAO  6083)12000(1 

'20  6083 

8,00  5917 

20 

d.  d.  

265   :  14Z.  Qs,  :  :  50  :  1^  19s.  5}d.      6083)118340(19 

6083 


57510 
54747 

n63 
12 

6083)33156(5 

30415 


2741 
4 


6083)10964(i 
6083 

4881 

Ans.  £.1   ]f:'^5|. 
SIMPLE  INTEREST  IN  FEDERAL  MONEY. 

The  principal  given  in  English  money,  and  the  interest  re- 
quired in  Federal. 

Rule.  Reduce  the  given  sum  to  shillings,  the  product  gives 
the  answer  in  cents,  and  the  pence  are  mills  nearly  ;  the  reason 
is,  that  at  6  per  cent,  per  annuni,  one  iitth  of  a  dollar  is  the 
annual  interest  of  a  pound  ;  that  is  20  cents  fcir  20  shillings,  or 
1  cent  for  every  shilling  in  any  given  sum. 

Examples. 

1.  Required  the  interest  of  jC.lp^  15  3  for  1  year  in  federal 
money. 

194  15  3 
20 

389,5  cents.  Ans.  38  duls.  95  cts.  3  mills* 


SIMPLE  INTEREST.  107 

2.     What  is  the  interest  of  £.129  13  2  ^or  2  years  in  fedcr^ 
al  money  ? 

129  13  2 
20 


I 


2593,2  for  1  year. 


518G,4  Ans.  51  dols.  S6  cts.  4  ms. 

3.  What  is  the  interest  of  £.91    12   1  for  5  years,  in  federal 
money  ? 

91    12   1 
20 


1832,1  for  1  year. 
5 


91,605  for  5  years.        Ans.  9I  dols.  60l  cts. 
4.  What  Is  the  interest  of  £.139  17  2  for  4  months? 

139   17  2 
20 


4  mo.   J  2797,2 


9,32,4  Ans.  9  dols.  32  cts.  4  ms. 


Principal  in  federal  ?no?iei/,  and  Interest  required  in  the  same. 

Rule.  INIultiply  the  principal  by  the  rate  per  cent,  and  as 
you  suppose  100  for  a  divisor,  point  otT  the  quotient  as  in  divi- 
sion ot  decimals. 

The  following  rule  answers  the  same  purpose. 

When  the  principal  is  dollars  only,  multiply  by  the  rate,  and 
from  the  product  point  off  two  figures  to  the  right,  the  figures 
to  the  left  hand  of  the  point  give  the  answer  in  dollars,  and  the 
rest  are  decimal  parts  or  cents. 

If  there  are  cents,  S^q,  in  the  principal,  multiply  by  tiie  rate 
and  point  off  as  above.  The  figures  to  the  lelt  ot  the  point  giv(5, 
theanswer  in  the  same  name  with  the  lowest  denomination  in 
the  principal. 


108  SIMPLE  INTEREST. 

Examples. 

5.  What  is  the  interest  of419  dollars  for  1  year  at()  per  cent.? 
419 
6 


25,14  Ans.  25  tlols.  14  cts. 

6.  What  is  the  interest  of  173  dollars  50  cents  for  1  year,  at 
€  per  cent.  ?  173,50 


Cents  1041,00  Ans.  10  dols.  41  cts. 

7.  What  is  the  interest  of  327  dols.  82  cts.  5  mills,  for  1  year, 
at  8  per  cent.  ?  327,82,5 

8 


mills     26226,00 

Ans.  26  dols.  22  cts.  6.  ms. 

8.     How  much  is  the  interest  of  325  dollars  for  3  years,  at  6 
per  cent,  per  annum  ? 

325  Or  thus,     325 

6  18  rate  for  the  time. 


19,50  for  1  year.  26OO 

3  325 


^8,50  for  3  years.  58,50 

Ans.  58  dols.  50  cts. 


tVhcn  the  time  is  months. 

Rule*  Multiply  by  half  the  number;  this,  as  was  before 
observed,  is  always  equal  to  the  rate,  for  the  time,  when  the  an- 
nual rate  is  6  per  cent,  per  ^nnum. 

Examples. 

9.  What  is  the  interest  of  284  dollars,  for  8  months,  at  6 
percent.?  284 

4 


11,36  Ans.  11  dols.  36ct3, 


ISIMPLE  INTEREST.  ie& 

10.     How  much  is  the    interest  of  187  dols.  25  cts.  for  l6' 
j>innths,  at  6*  per  cent,  per  annum  ? 
187,25 


Cents  1498)00  Ans.  14  dols.  98  cts. 

1 1.     What  is  the  interest  of  95  dollars,  for   2  months,  at  6 
|)er  cent,  per  annum  ? 

1 

,95  Ans.  Q5  cents. 

12.     How  much  is  the  interest  of  126  dollars,  46  cents,  for 
9  months,  at  6  per  cent.  ? 

126,46 
H 

505,84 
63,23 


Cents     569,07  Ans.  5  dols.  69  cts. 

13.  How  much  is  the  interest  of  124  dollars,  for  1  month, 
■Jit  6  per  cent.  ? 

^)124  Or  124 

"  —  ,5 

,6^ 

,62,0  Ans.  62  cts. 

14.  What  is  the  interest  of  69^  dols.  84  cts.  fer  9  months*, 
tit  10  per  cent,  per  annum  ? 

694,84  Or  694,84 

10  7|=rate  for  the  time. 


Cents  6948,40  for  2 

6    1  3474,2 
a    1  1737,1 

I  year  4863,88 
347,42 

dols» 

a  cts. 

3 

Cents  52,11,30 

Ans.  52 

52,11,3 

K 

in. 

J!  10  SIMPL]-:  INTEREST. 

^■>.   ■  How  n'>.iir]j  h  the  amount  of  985    dollars,  for  5  ycirs 
■'i  8  moijths;  iit  0' per  cent,  per  annum  ? 

r>4  half  the  months. 


2^}35 


334,90  infcrosf, 
f/85,        principal. 


1310j5)0  amount.     Ans.  1319  dols.  C/0  cts. 


Vv'hen  tlic  time  Is  months  arui  day«,   and  llie  annual  rate  6  per  cent. — rjul- 

ti])h  ijy  Iialf  liie  nioiitlis  and  one  sixth  of  the  days,  which  is  equal  to  tlie  rate, 

tor  \\i:  <,;ivcn  time,  and  separate  one  figure  to  the  right"  ibrihe  decanal  in  the 

iL',  and  proceed  as  usual.     Should  there  be  a  remainder  in  taking  a  sixth  of 

.:•  days,  reduce  it  to  a  vulgar  fraction ;  this,  and  not  the  dccimai^  will  always 

_.. ve  the  exact  rate.  •  •  •  •  ^ 

Examples. 

l6.     V/hat  is  the  interest  of  194  dols.  for  4  months  and  12 
days,  at  6  ])ei-  cent.  ?  (lol.s. 

9?K  V?,  1:,2  — tothe  rate,  found  by  the  rule, 

12  :  6   ::    4,4  or  the  annexed  calculation. 

6  388 

388 

12)26,4 


4,2G,8 
2,2  Ans.  4  dols.  2()  cts.  8  m-s, 

17.  How  much  is  the  interest  of  263  dollars,  48  cents,  for  2 
months  and  21  days,  at  6  per  cent.  ? 
dols.    cts. 
263,48 


i,3i 

7904 1 

2u3-i-8 

13174 

Ccnt^  S5  ,(-^8     Ans.  3  uoh.  55  cV^.  6  n\s. 


SI MTLE  INTEREST.  1 1 1 

IS.     How  much  is  the  interest  oi'olS  dols.  for  10    moiulis 
mid  i'S  days,  at  6  per  cent.  ?    . 
318 


6:}6 


t  ]0{) 

\  IOj 


dols.      10,7-1,8  Ans.  iG  dols.  7-i'  cts.  8  m. 

10.     What  is  the  inlerest  of  -ili^  doL;.  for  1  ^ccir,  7  months, 
and  ]/  days,  at  6*  per  cciit.  ? 

4:8  418 

dols.      4  0,S<);V  A:is.  40  doh,.  83  cts.  4  m. 

i20.     How  imich  is  the  iiUcrcst  of  '208  dois.    44  cti.    for    3 
ytViTS;  J  ijionihb,  aud  2o  days,  at  6'  per  ceut,  r 
208,44 


V!;\!0 

bl&7. 

^^0 

1 

=r34S 

(AMits     6()1:;,;34,4       Ans.  5o  doU.  l!}cts.  5m. 
•  1.      What  is  the  interest  of  I  dollar,  for  18    days,  at  6*    ];cr 


c-ent.  ? 

1 
,3 


,00, J  mills.  Ans.  3  mills. 

One  niiirre  i^  j-or;ir:i(ocl  for  the  decimal  'wi  th'Mnultiplicr,  and 
tv.'C)  cyp.hvr^  w:  1  and  pointed,  uccoitlini;,  to  the  ^eneial 

rul  e. 


i  12  SIMPLE  INTEREST. 

22.     What  is  the  interest  of  910  dols.  50  cts.  for  3  years,  ^ 
Kionths,  and  2()  days,  at  7  per  cent,  per  annum  ? 

910,50 

7 


63,73,50 
3 


Or 

thus,  910,50 

22,9J 

8 19450 

182100 

182100 

*s. 

30350 

191,20,5  for  3  years. 

6' mo.      I    31,86,7  

3  mo.       I    15,93,3  ■J)208,80;S010at5per  cent. 

15davs     i      2,65,5  34,80,1 

lOdnys     -J       1,77,0  . 

1  day      /o       ?17?7  tlols.  243,60,9  at  7  per  cent. 

dv/is.   243,60,7  Ans.  2-13  dols.  60  cts.  8  nis. 

23.  How  mucli  will  1.85  dols.  26  cts.  amount  to,  in  2  years, 
3  months,  and  1 1  days,  at  7k  P^'^  cent,  per  annum  ? 

Ans.  216  dols.  94  cts.  4  ms. 

24.  What  is  the  interest  of  57  dols.  78  cts.  for  1  year,  4 
months,  and  17  tl ays,  at  4  per  cent,  per  annum  ? 

Ans.  3  dols.  I9  cts. 

25.  How  much  is  the  amount  of  298 dols.  5Q  cts.  from  19th 
May,  1797,  to  the  1  ith  of  August,  1798,  at  8  per  cent,  per  an- 
num ?  Ans.  327  dols.  98  cts.  4  ms. 

26.  How  much  is  the  amount  of  I96  dollars,  from  June  14, 
17.9s?  to  April  2[)j  1799?  ^t  5:|  per  cent,  per  annum  ? 

Ans.  205  dols.  86  cts. 

27.  Vvhat  is  the  interest  of  658  dollars,  from  January  9  to 
Qctober  9  following,  at  h  per  cent,  per  month  .? 

Ans.  29  dols.  61  cts. 

Ja  the  calculation  of  inlcrcst  in  federal  money,  thus  far,  the  year  is  siippov 
p(l  to  be  It>  months  of  SO  days  each,  making  it  only  360  days.  Most  persons- 
Tise  this  method  of  computing  the  time,  but  as  it  is  5  days  less  in  a  year  than 
the  tr-iie  number,  some  merchants  calculate  by  days,  without  any  regard  t» 
vuQiiUis,  as  being  more  accurjilc. 


SMMPLE  INTEREST'.  US 

Examples. 
2^;  What  is  the  interest  ot  7 0S6' dollars,  for  39 days,  at  0  per' 
c^nt.  per  aniiuui  ? 

By  Compound  Proportion. 
7086 
39 

63774 
21258 

dols.  cts. 

6083)276.154(^45  43 
2-J  332 

J^  *''  "*  33034 

30415 

26190 
24332 

185^0 
18249 

331  Ans.  45  dol.s.  43  ctd, 

i20.     Wliat  is  the  interest  of  87  dols.  oGcts.  for  72  days,  at^ 
6  per  cent,  per  ^.nniHn  ? 

07,56 
72 

17512 

61292 

cts.  m. 

€083)6304,32(103  6^ 
6083 

22132 
18249 

38830 
36498 

2342  Ans.  Idol.  3clff.  6ni. 

fids.  cts.  daiiK  dots,  cts,  m»' 

30.     2962  li^  for    2.S4  at  6  per  cent,  per  ami.       "  Ans.  123  68     8 

o  J .         S5  256 147     2 

32.  1733  97  102 29     7     5' 

33.  455  52  47 3  51     9  ' 

34.  215  80  125 4  43     4^ 

35.  517  90  84 7  15     I 

56.  73  63               92 1  H .  5  > 

K2 


tli  SIMPLE  INTEREST. 

The  following  method  of  calculating  the  interest  upon    ac- 
counts,  when  there  arc  partial  payments,  is  sometimes  used. 

1798.  dols.  days.        Prod.princ.i^'tinw, 

Janaanj  2,  Lent -100  on  interest  for   13  » loOO 

^13,  Lent 110 

"^  .  '      "^0 * '5. -lOoa 

20,  Received  l62  * 


48 14 672 

Febn/an/ 3,  hcnt 95 

143  ••.-  7 to5r*^ 

10,  Received    .90 

53   6*0 318 

iGjLeni- ISG 

239  1©........2390 

' 26, Received    70 


169 3 507 

March     1,  Lent 250 

419 2..,. .. ..    S3% 

3;,  Received  2/0 


1.49 10....  «...  1490 

13,  Received  143 

20,  Time  of  adjustment  6  ............   7 ....... .      42 

96O8 
d.  cfs. 
Then  (J083)9608(   1,57  interest  at  6  per  cent. 
60S3     6,       the  principal  due. 

35250  7,57  the  amount  due  March  20th. 
30415 

48350 
425^1 

^76'9 


SIMPLE  INTEREST,  .  Ilj 

By  this  method  interest  may  be  calcuhited  on  accounts,  mul- 
tiplying each  sum  by  the  days  it  is  at  interest,  and  taking  the 
(quotient  of  36500,  divided  by  the  rate  per  cent,  as  a  fixed  di- 
visor to  the  sum  of  the  products.  Thus,  the  rate  in  the  hist 
example  being  6  per  cent,  the  divisor  is  (j083  ;  for  5  per  cent, 
it  would  be  7300  ;  for  7  per  cent.  5214,  &c. 

If  the  time  '\^  months^  multiply  each  sum  by  the  months  it  is 
at  interest,  and  take  the  quotient  of  1200,  divided  by  the  rate 
as  a  divisor.  Thus,  for6  per  cent,  the  divisor  is  200  ;  for  5  per 
cent.  240  ;  for  8  per  cent.  150,  &c. — {See  Compound  Propor-- 
iio?iy  page  73') 


m  COMPUTING  INTEREST  ON  NOTES,  S^c. 

It  has  generally  been  the  custom  to  find  the  amount  of  the 
principal  from  the  time  the  interest  commenced  to  the  time  of 
settlement,  and  likewise  the  amount  of  each  payment,  and  then 
deduct  the  amount  of  the  several  payments  from  the  amount 
of  the  principal. 

Example. 

A,  by  his  note  dated  April  25th,  179^,  promises  to  pay  to  B 
774  dolji.  7^  cts.  on  demand,  with  interest  to  commence  4  months 
after  the  date.     On  this  note  are  the  following  endorsements  : 

Received, Ocf.  12th,  1798,  260do\s,  igcis.—Oct,  13th,  1798, 
60  dols. — Nov,  2,  1 79S,  200  dols.  And  the  settlement  is  made 
Dec.  15  th,  1798. 

Calculation. 

doh.  ctx. 

The  principal  carrying  interest  from  25th  Aug.  1798 •  •  •  •. 774   76 

Interest  to  Dec.  15,  1798 (3  ni.  20  days) 14  20 

Amount  of  the  principal  • 788   96 

dols.  cts. 

First  payment,  Oct   12t]i,  1798 260  19 

Imerest  to  Dec.    15tli,   1798 (2  ms.  3  days) . . 

Secowd   payment,   Oct.    13th,    1798 ■ 

Interest   to  Dec.  15th,  1798 (2  m».  2  days)  • . 

Third   payinenl,  Nov.   2,   1798 ■ 

iQterest  to  Dec.  15,  1798 (1  m.  13  days). 

Amount  of  the  payments • 524  97 

SeUlement  is  made  for D<?//ar«— 263  99 


.     2 

73 

60 

00 

0  62 

200 

00 

1 

43 

1 16  SDIPLE  INTEREST.- 

RULE  cstahli^:hi'd  by  the  Courts  of  Law  in  Massachuscii s  fay 
?iiakifig  up  judgments  o/i  sfxurities  roii  money,  wv^/c^  arc 
vpon  Intercity  and  on  iilneli  partial  payments  have  been  endorsed. 

Compute  tlic  interest  on  tlie  principal  sum,  from  the  time 
when  the  interest  commenced  to  the  first  time  when  a  pjiyment 
uas  made,  which  exceeds  either  alone  or  in  conjunction  with 
tlie  preceding  payments  (if  any)  the  interest  at  that  time  due: 
add  that  interest  to  the  principal,  and  from  the  sum  subtract 
the  payment  made  at  that  time,  together  with  the  preceding. 
j)avnK'nis  (if  an\/)  and  the  remainder  forms  a  new  principal  ^^ 
on  winch  compute  and  subtract  the  interest,  as  upon  the  first 
principal :  and  proceed  in  this  manner  to  the  time  of  the  judg- 
ment. By  this  Rule,  the  payments  are  first  applied  to  keep 
down  the  interest;  and  no  part  of  the  interest  ever  forms  a  parfe- 
of  a  principah carrying  interest. 

The  following  examiple  will  illustrate  the  rule,  in  which  the 
interest  is  computed  at  the  rate  of  6  per  cent,  by  the  year,  that 
being  the  legal  rate  of  interest  in  INIassachusetts. 

A,  by  his  note  dated  January  1, 17S0,  promises  to  pay  B  lOCO 
dols.  in  six  months  froui  the  date,  with  interest  from  the  date* 

On  this  note  arc  tlie  followiaig  endorsements  :  • 

Received,  Aprill,  1780,  24  dols. — August  1,  1780,  4  dols. — 
Dec.  1,  1780,  6  dols.— Fe/;.  1,  1781,  60  dols.— Jz//j/  1,  1781, 
40  dols.— /////c  1,  .1784,  .300  doXs.—Scpt,  1,  1784,  12  dols.— 
Jan.  1,  1785,  15  dols.  and  Oct.  1,  1785,  oOdols.— and  the 
judgment  is  to  be  entered  Dec,  1,  179^. 

Calculation. 

Tho  principal  sum  carrying  interest  from  January  1,  1780 1000  00 

I.ncrcst  10  April  1,  1780,  ^(3  months) 15  00 

Amount     10 Id  00 
Paid  April  1,  1780,  a  sum  exceeding  the  interest      24  00 

Ilemaindv?r  for  a  new  principal •  •  •       ^'-^1   ^^^ 

Interest  on  991  d^jis.  from  April  1,  1780,  to  Feb.  1,  1781,  (10  mo.)      49  55 

Amount     1040  55 
raid  August  1,  1780,  a  sum  less  than  the  interest  then  due  Dts.  4  00 

Paid  Dec.  1,  1780,  do.    do. 6  00 

raid  Feb.  1,  1781,  do.  greater  than  the  iiUerest  then  due    60  00 

70  00 


SIMPLE  INTEREST. 


117 


Remainder  for  a  new  principal   •  •  •  • "• 

Interest  on  970  dois.  55  cts.  irom  Feb.  1,  1781,  to  July  1,    1781, 
(5  monlhs) • 


Amoiu^.t 


Paid  July  1,  1731,  a  sum  exceeding  the  interest 


Ilemainder  for  a  new  principal    ««.►-♦ 

latere;^!  on  95 1  dols.   81  cts.  from  July  1,  1781,  to  June  1,  1784, 
(2  years  1 1  months)    • • •  • 

Amonnt 
Paid  June  1,  1784,  a  sum  exceeding  the  interest 


Ilemainder  for  a  new  principal 

Interest  on  821  dols.  90  cts.  from  June  1,  1784,  to   Oct.  1,   173.5, 
( 1  year  4  months)     • 

Amount 
Tnid  Se^.  1, 1784,  a  s-nm  less  than  the  interest  tlicn  due,  Dh.  12  00 

Paid  Jan.  1, 178.5,     do do. 15  00 

Paid  Oct.  1,  1785,     flo.  greater  with  two  last  payments  than 

interest  then  due • • 50  00 


dnh. 

cts. 

970 

55 

?4 

26 

994 

81 

40 

00 

9.54 

81 

167 

09 

11^1 

90 

300 

00 

821 

90 

65 

7.J 

887  65 


Remainder  for  a  new  principal    • 

Interest  on  810  dols.  65  cts.  from  Oct.  1,  178.5,  to  Dec.  1,   1790, 
the  time  when  judgment  is  to  be  entered  (5  years  2  months) 


Judgment  rendered  for  the  Amount 


77  00 
810  65 

1251  SO 
1061  95 


^  TABLE, 

Shcxiiiig  the  7iumher  oj^ Days,  from  any  Day  in  any  Month ^  to  the 
sa7ne  Day  in  any  other  Month,  through  the  Year, 


From 

Jan.leb.  Alar.Ap.  May. 

Jun. 

July.Auii.Sep  Oc. 

Nov 

Dec 

JuJdn 

io651.S.54|o06ji!75|'^45 

'214 

1 84 1 1.53  IV^I   9'2 

61 

31 

Feb 

1   3l|:36>|:i-7r|.>06|276 

^.M5 

215J181  1.5o|12o 

92 

62 

^vJht 

1   .0^1    L'8j.:i65|a:;4|o04 

■^4312  r2jl8l|  151 

12(? 

90 

Apr. 

j   90 1   .59|   31 1. -565 i.->>5! 

:^04 

'274|24:i  21i?  18y 

151 

121 

^   ;v»a^V 

r^uj  89    01 1  :yj  ,io5 

SoO 

;i04  27.5  -X4'-J 

212 

18; 

1->1 

Jun- 

151|1^^0    n\  61 

.Sl( 

S6o 

o35  304127.5 

243 

212 

182 

.fuiv 

1 181  |l.5(»i  1^221    91 

61| 

tiCi 

S65I334|.N0.5 

273 

'>42 

^212 

AUL'. 

|-21/(18l|l5^:|lt^'^|    9t^ 

bl 

3l|o6.)|^c*4io0'l 

27.> 

2-13 

^vpX. 

l-:i4;.|2l'L'|184jl5.S  lii.S 

9-^ 

6v     31(3651335 

.31  ;4 

-'?4 

Uil. 

|-V:)i-r4^^|i^l4il85  15o, 

1-- 

92     61 1   30|:»65 

:rM 

>{)4 

Nov. 

\r>{H\^^7S\<245  2l4|l8]i 

15.1 

123}    92 1   61 1   :^)\ 

365 

.S35 

Dec. 

|;3:]4|:io:iii^75  V4i|ji4| 

]8:,i 

153:1221    91 1    61 

30 

36.0 

IIS 


SIMPLE  INTEREST. 


THE     USE   OF  THE  TABLE. 

Suppose  the  number  of  days  between  the  Gci  of  .May  and 
3d  of  November  was  required  ;  look  in  the  coliinjn  under  M 
for  November,  and  against  that  month  you  will  iind  184. 

If  the  given  days  be  different,  it  is  only  adding  or  subtracting 
tlieir  inequality'  to  or  from  the  tabular  number.  Thus,  from 
May  3d  to  Nov.  37th  is  184--f  Urz  I98  days,  and  from  Nov. 
J 7th  to  May  3d  is  181 — 14-  — 167  days. 

If  the  time  exceed  a  year,  305  days  must  be  added  ;  thus 
from  the  4th  of  February,  17i)8,  to  the  4th  of  Sept.  1799,  is 
212-f  5()5=:577  days. 

IV'OTK.  Ill  leap  years,  if  ilie  end  of  tiie  month  of  Febraarj  be  in  the  lime 
©ftj  day  niu^t  be  added  on  ihat  account. 


COMPOUND  INTER  EST 

Is  that  which  arises  both  from  the  principal  and  interest^ 
that  is,  when  the  interest  on  money  bccoines  due,  and  not  paici, 
it  is  added  to  the  principal,  and  interest  is  calculated  on  this 
amount  as  on  the  principal  before. 

Kltli:.  Find  the  simple  intere^-t  of  the  glv<*n  sum  for  one-yenr,  and  add  it 
to  the  principal,  and  then  find  liic  interest  lor  tlitit  amoiitit  ior  ijjo  next  year, 
and  so  on  for  ihe  number  of  years  recji^uired.  Subtract  the  priacipal  from  the 
lii<t  aiu'junlj  and  the  remainder  will  be  t!ie  comijouud  inlcrei,l. 
Examples. 
1.  V/hat  is  the  interest  of  £,2^  l-is.  6(1.  for  3  years,  at  6 
per  cent,  per  annum  ? 

6 

8-7 

,  -  >  first  year's  intere^it. 
4    j 


?46'    14 
12     6 

'2     9 


261    1  b     0  h   a  mount  o  f  t  h  e  i\  rs  t  \-  ea  r . 
13      1      6[]  ,  ,    •    .\ 


IJ7     4      4-4   amount  of  the  sec 
13    17      2',  7 
2    15      5ii 


third  year's  intcrc:: 


293    17      0  amount  of  the  third  year. 
24(i    14     6  iirst  piineipal. 


0"  comiponnd  interest  for  3  years. 
Ans.  .t'.47    2..V.  CfL 


CO^IPOUND  INTEREST. 


119 


.   Wluil  is  the  compound  interest  of  £.760   10^.  ror4ycars, 
t Ju  per  cent,  per  annum  ?  Ans.  £,\99   12*-  2(/. 

^^3.  How  much  is  the  amount  of  £.1^8  17 s,  6d.   for  0'  years, 
?it  0  per  cent,  per  annum,  compound  interest  ? 

Ans.  £.182   \6  2|. 
4.  How  m.uch  is  the  amount  of  500  dolhirs,  for  3  years,   at 
^  per  cent,  per  annum,  compound  interest  ? 
'       ^       500, 


1 


1 

i  0 
1 
3 


'ih'-' 


interest. 


530, 

"  ''^^  >  second  interest. 
5,.:.0  3 


5 

1 

Q  0 

561,80 

1 

1 
5 

28,09 
5,6"1| 

)  third  interest. 

595, 50j  the  amount  required.  Ans.  595  d.  50|  c. 

5.  What  is  the  amount  of  629  dols.  ior  7  years,  at  6'4)er  cent, 
per  annum,  compound  interest  ?        Ans.  94-5  dols.  78  cts.  3m. 

6,  How  much,  is  the  compound  interest  of  1256  dols.  for  15 
years,  at  6  per  cent,  per  annum  ?      Ans.  1754-  dols.  6  cts.  6  m. 

A   TA  RLE  shewin<:^  the  amount  of  ^it  pound  or  one  dollar  for  any  moi'her  of 
Ijcays  under  :>.:3,  at  the  rates  nf  5  find  6  per  cent,  per  ami.  compound  interest. 


Veins. 

5     Rates.     6 

Years 

5     Rates.     6            j 

1 

1,05000 

1,06000 

17 

2,29201 

2,69277 

2 

1,10J50 

1,1 '2:360 

18 

2,40662 

2,85434 

3 

1,15762 

1,19101 

19 

2,52695 

3.02.559 

4 

1,'>15.")0 

1,26'247' 

20 

2,65329 

3,20713 

5 

1,'276  28 

l,3o8i?2 

21 

2,78:V96 

3,39956 

6 

1,. J  1009 

1 ,4 1 852 

!     22 

2,92526     \ 

3,60353 

7 

1,40710 

1,50.-163 

23 

3,07152 

3,81975 

8 

1,4774) 

],;39584 

24 
25 

3,V2510 

4,04893 

9 

l,55i:i^i 

1,63948 

3,38635 

4,29187 

10 

1,62089 

1,79084 

i     26 

S,h5b67 

4,.54938 

11 

l,710o'4 

1,898'<>9 

1     27 

3,73345 

4,82234 

n 

1,79^85 

2,01219 

i     28 

3.92013 

5,11168 

13 

1,B8')65 

2,13292 

29 

4,11613 

.5,41838 

li 

l,9799r» 

2,26090 

30 

4,32194 

.5,74349 

15 

2,07  89^i 

^,fi^655 

31 

4,53804 

6,08810 

\6 

*?.18'J87 

2,510.')5 

32 

4,76494 

6.45338 

The  use  of  this  Table  is  pl«ia  aud  easy,  for  multiplying  t!ie  f^mires  standing 
against  tjie  number  of  years,  by  the  given  piiacipal,  the-jproducl  is  (he  amuunt 
required. 


120  COMPOUND  INTEREST.  1 

Examples. 

7.  AVhat  is  the  amojint  of  500  dollars,  for  3  years,  at  6  per 
€cnt.  compound  interest  ? 

1,19101    the  tabular  number  for  the  time. 
500  the  principal, 

595,50500 

Ans.  695  doh.  50  cts. 

8.  A  merchant,  on  inspecting  some  old  accounts  in  March, 
1799)  fi"fis  a  settlement  dated  March  1771,  by  which  it  ap- 
pears there  is  due  from  him  to  A.  B.  £.2  8a.  this  sum  be  pays 
with  compound  interest  at  6  per  cent,  per  annum.  The  amount 
of  it  is  required  ? 

5,111(38  the  tabular  number  for  28  3^ears. 

2,4  the  principal  with  the  shillings  inserted  decimally. 


2044672 
1022336 

£.12,268032 

20 

■  % 

s,   5,360640 

12 

(L  4,327680 
4 

^rs.  1,310720     Ahs.  £.12  5s.4ld.  or  40  dols.  89  cts.  Shis, 

Calculated  in  Federal  Money. 
5,11168 

8  dollars. 


Ms.  40,89344 


Ans,  40  dols.  ^9  cts.  3  mills,  as  above. 


COMMISSION  AND  BROKERAGE. 


Kl 


COMMISSION A^jy  BROKERAGE. 

Commission  and  Brokerage  are  compensations  to  Fac- 
tors and  Brokers  for  their  respective  services. 

The  method  of  operation  is  the  same  as  in  Simple  Interest. 

Examples. 
1.  What  is  the  commission  on  £.59^  18  4,  at  6  per  cent.  ? 
59(3"   18  4-         Or  thus,  £.5 


35181    10  0 
20 


16Y30 
12 

3|6'0 
4 


A 

596   18 

4. 

i 

29    16 
5    19 

II 

4i 

£.35   16 

^2. 

214-0  Ans.  £.55   16  3^ 

2.  What  is  the  commission  on  1974  dollars  at  5  per  cent.  ? 
197^ 


9S,70  Ans.  98  dols.  70  cfs. 

3.  Wluit  : ;  the  commission  on  £.525  11   5  at  oh  per  cent. ) 

Ans.  £.18   8  7 

4.  What  is  the  commission  on  £.1258   17  3  at  7%  per  cent.? 

Ans.  £.93  3   14. 

5.  What  is  the  commission  on  2176  dols.  50  cents,  at  2|  per 
cent.  }  Ans.  54  dols.  41  cts.  2  m. 

6.  The  sales  of  certain  (];oods  amount  to  1873  dols.  40  cts, 
what  sum  is  to  be  recciv(vl  ibr  them,  allowing  2|  per  cent,  for 
commission,  and  \  per  cent,  for  prompt  payment  of  the  neat 
proceeds  ?  Ans.  1821  dols.  99  ct5.  9  m. 


V22  COMMISSION  AND  BROKERAGE. 

7.   Required  the  iicat  proceeds  of  certain   j^oods  amoimtiii^ 
to  .€.456    118,  allowing  a  commission  of  2|  per  cent. 
£,5      A  i  456   11      8 


I   j     22   16"     7  commission  at  5  per  cent. 

11      S     3j  commission  at  2h  per  cent. 


Ans.  ^\445     3     4|  neat  proceeds. 

S,  Vvhat  is  the  commission  on  .£.1371   9  5  at  5  per  cent,  f 

kns.  £f)S   11   5J 
9.  What  is  the  commission  on  £.1958  at  5  J  per  cent.  ? 

Ans.  £.107  13  9h 
iO.  What  is  the  commission  on  £.1859  7  6  at  |  per  cent.? 

Ans.  £.16  5  4^ 

11.  W^hat  is  the  brokerage  on  1853  dols.  at  |  per  cent,  f 

Ans.  13  dols.  89  cts.  7  ms. 

12.  What  is  the  brokerage  on  £.874   15  3   at  J  percent.? 

Ans.  £.2  3   8| 

13.  What  is  the  brokerage  on  129S  dels*  53  cts,  at  |  per  cent.  ? 

1298,53 
3 


8)3895,59 

Doh,     4,86,94  Ans.  4  dols.  86  cts.  9  m. 

14.  What  is  the  brokerage  on  £.1321   11  4  at  ij  per  cent.? 

Ans.  £.14   17  4 

15.  A  factor  receives  988  dollars  to  lay  out,  after  having 
deducted  his  commission  of  4  per  cent,  how  much  will  remain 
to  be  laid  oufc  ? 

d. 
100 
4 

d.  d.  A 

If   104:  100    :  :    988  :  950  dols.  the  ans wer*| 

16.  A  factor  has  in  his  hands  369O  dollars,  which  he  is  di- 
rected to  lay  out  in  iron,  reserving  fn^^m  it  his  commission  of 
2  J  percent,  on  the  purchase  ;  tlie  iren  being  9^  dols.  per  ton: 
liow  much  did  he  purchase  ? 

Ans.  37  tons  17  cwt.  3  qrs.  161^9  lb. 


INSURANCE.  t^o 

INSURANCE. 

Insurance  is  an  exemption  from  liazard,  by  paying,  or 
©tbciwise  securing  a  certain  sum,  on  condition  of  being  indem- 
liified  for  loss  or  damage. 

Policy  is  the  name  given  to  the  instrument,  by  which  tie 
eontract  ot  indemnity  is  efixicted  between  the  insurer  and  insured* 

Average  loss  is  5  per  cent. ;  that  is,  if  the  insured  suffer  any 
loss  or  damage  not  exceednig  5  per  cent,  he  bears  it  himicli",. 
and  the  insurers  are  free. 

Rule.     The  method  of  operation  as  in  interest. 

Examples. 

1.  What  is  the  premium  of  insuring  c€.924  at  7  per  cent,  t 

Ans.  ^'.64   13  7 

2.  What  is  the  premium-  on  i650  dollars,  at  12  per  cent.  ? 

Ans.  198  dols. 

3.  What  is  the  premium  of  insuring  1250  dollars,  at  7  5  per 
cent.  ?  Ans.  93  dols.  75  cts. 

4.  What  is  the  premium  of  insuring  4500  dollars,  at  25  per 
cent.?  Ans.  1125  dols. 

5.  What  is  the  premium  of  insuring  l650  dollars,  at  15  J 
per  cent.  ?  Ans.  255  dols.  75  cts. 

6.  What  is  the  premium  of  insuring  1873  dollars,  at  -J  per 
cent.  ?  Ans.  2  dols.  34-  cts.   1  m. 

7.  What  sum  is  to  be  received  for  apolicy  of  l658  dols.  de* 
ducting  the  premium  of  23  per  cent.  ?  Ans.  1276  dols.  66  cts, 

8.  What  sum  must  a  policy  be  taken  out  for  to  cover  1800^ 
dollars,  when  the  premium  is  10  per  cent.  ? 

100  policy. 

10  premium. 
r?.        d.  d. 

90  sum  covered.     If  90  :  100  :  :  1800     Ans.  2000  dots.. 

Troof,      2000  dollars  at  10  per  cent. 
10 


200,00  the  policy        2000 

the  premium      200 

sum  covered    1800  dols. 

9.     What  sum  must  a  policy  be  taken  out  for  to  cover  39^6 
dola.  7  cts.  when  the  premium  is  6  per  cent.  ? 

Ans.  4176  dols.  67  cts. 


iJl  GENERAL  AVERAGE. 

GENERAL  AVERAGE. 

Whatever  the  master  of  a  ship  in  distress,  with  the  ad- 
vice of  his  officers  and  sailors,  deliberately  resolves  to  do,  for 
tlic  preservation  of  the  whole,  in  cutting  away  masts  or  cables, 
or  in  throwing  goods  overboard  to  lighten  his  vessel,  which  is 
ivhat  is  meant  by  jettison  or  jetson,  is  in  all  places  permitted 
to  be  brought  into  a  general  average,  in  which  all,  who  are 
concerned  in  ship,  freight  and  cargo,  are  to  bear  a:i  ecjual  or 
proportionable  part  of  the  loss  of  what  was  so  sacrihced  for  the 
common  w  elfare ;  and  it  must  be  made  good  by  the  insurers 
in  such  proportions  as  they  have -underwritten. 

EXAMPLES  OF  ADJUSTED  AVERAGES. 

1.  A  loaded  ship  met  with  such  bad  weather,  that  the 
raaster  and  mariners  found  it  impossible  to  save  her  without 
throwing  part  of  her  cargo  overboard,  which  they  are  authori- 
i:ed  to  do  \oi'  preservation.  Being  thus  necessitated ^  they  threw 
.such  goods  as  lay  nearest  at  hand,  and  lightened  the  ship  of 
10  casks  of  hardware,  and  40  pipes  of  Madeira  wine,  which 
they  judged  suflicient  to  keep  her  from  sinking.  Soon  after 
that  the  ship  arrived  at  her  destined  port,  and  then  an  average 
bill  was  immediately  made  in  order  to  adjust  the  loss,  and  to 
pay  the  proprietors  of  those  goods,  which  were  thrown  over- 
board, for  the  good  of  the  whole. 

Average  accrued  to  ship ,  for  goods   t/wcnvn  oierboard  for 

presertatio/i  of  ship,  freight  and  cargo. 

Dnh. 

Ship  valued  at 12000 

Freight  (wages  and  victuals  deducted) SOOO 

Thomas  Kugeiit's  vahie  of  goods 4000 

Thomas  Morgan's  vahie  of  goods       ^rA)0 

James  Simpson's  value  of  goods • 8500 

Andrew  Wilson  for  40  pipes  of  wine 4000 

Laurence  Ward  for  10  casks  of  hard  ware 600O 

40000 

Dch. 
JsFr.  AinJrew  Wilson's  goods  thrown  overboard  were  valued  at  400l> 

Mr.  Laurence  Ward- do.  •  • 6000 

10000 

1140000  give  10000  loss,  what  loss  will  100  give  ? 

Ans.  25  per  cent. 


GENERAL  AVERAGE.  12S 

The  ship  must  pay  to  A.  W.   and  L.  W.  for  12000 

dollars,  at  25  per  cent.     • 3000  ^ 

The  freight  3000  dollars,  at  the  same  rate 750 

Thomas  Nugent,  for  4000  dollars,  at  the  same  rate  1000 
Thomas  iMorgan,  for  2500  dollars,  at  the  same  rate       6'25 

James  Simpson,   for  8500  dollars,  at  the  same  rate  2125 

A.  W.  and  L.  W.  receive  of  the  owners  of  the  goods  saved, 

and  the  ship's  owners 7-'''00 

Their  property  being  insured,  the  underwriters  pay  them     2500 

loooa- 

2.     The  Sea  Horse,  capt.  Dix,   laden  with  h^mp^,   cordage, . 
and  iron,   bound   from  Riga  to  Boston,   ran  on  shore,  coming 
through  the  grounds  at  Elsineur.     The  captain   Ivired  a  great 
number  of  men,  and  several  lighters,  to  lighten  the  ship,   and 
to  get  her  afloat  again,    which  was  done  ;    but  he  was  obliged 
to  pay  409  dols.  23  cts.  for  their  assistance.      This  expense  be-  - 
ing  incuircd  to  preserve  both  ship  and  cargo,  the  average  must. 
coiise(juently  be  general.     When  the  ship  arrived   at  Boston, 
the  captain  immediately  made  a  protest  and  an. Average  bill,, 
which  was  thus  stated  : 

Average  accrmng  to  the  ship  Sea-IIorse  from  Riga  to  Boston^  in  • 
^^ 99yfof  cisai^tance  in. getting  oj/'  the  strand  of  ELineur. 

dels,  cts,  . 
For  sundry  charges  paid   at  t?he  Sound  for  lighters  and 

assistance  in  getting  ofl'  the  ship    •  •• 409  ^^  ' 

Protest  and  postage  .•..*..•...•.  /^  »...,*• 35  37 

444   b'O. 

Tlic  ship's  freight  money 34()0 

Wages  for  all  the  people,  (4  ms.  and  20  d.)  5()0  7  ^ 

Victuals  for  ditto    .....,*....... 300  |  ^"® 

2()00 

The  ship  Sea-Horse  valued  at  •  •  • . . .  ......  ....  ICOOO 

Freight  valued  at o^'co 

W  liham  Jenkins  for  value. of  hemp 1SO('0-. 

Daniel  Jones  fur  value  of  cordage     400O 

iiEOch  Fiinn  lor  value  of  iron  • ..... 2400 

L2-  3<;oao-» 


V26  gkni:ral  average. 

Jf  3900,0  dols.  lose  44-ldolb.  60  cts.  what  will  100  dols.  lose  ? 

Ans.  1  dol.  14  cts. 

dots.  cis. 
Theship  must  bear  12000dols.  at  114  cts.  per  lOOdols.    136  Sa 

The  freight  2600  dols.  at  the  same  rate 29  64»    j 

William  Jenkins  for  1 8000    • 205  20  J 

Daniel  Jones  for  4000    45  6Q 

Hjlmch  Flinn  for  2400 27  36' 

444  60 


BUYING  AND  SELLING  STOCKS, 

Stock,  in  the  sense  in  which  it  is  here  used,  is  a  fund  es- 
tablished by  government  or  individuals  in  a  corporate  capacity, 
tte  value  of  which  is  variable. 

Examples. 

1.  What  is  the  amount  of  1565  dollars  national  bank  stocl?^^ 
at  134  per  cent.  ? 

1565 
134 

"6260 
4695 
1565 

2097,10  Ans.  2097  dols.  10  cfs. 

2.  What  is  the  anaount  of  2958  dols.  bank  stock,  at  25  per 
cent,  advance  ? 

2958 
25     J     739.50 

3697,50  Ans.  3697  dols.  50  cts. 

dols-,  dols.  els, 

3.  6959  of  8  per  cent,  stock,  at  1 10  percent.     Ans.  7654,90 

4.  1796       6 91 1 1643,34. 

5.  1 284        3 54| 696,57 

6.  3172        deferred    89    2823,08 

7.  1518        state  notes 83^ 1271, 32j. 

«.  1086       UnioaBank 128    215S;0a 


DISCOUNT.  127 


DISCOUNT 

Is  the  abating  of  so  much  money  to  be  received  before  it  k 
due,  as  that  money,  if  put  at  interest,  would  gain  in  the  same 
lime  and  at  the  same  rate. 

Thus  100  dollars  would  discharge  a  debt  of  106  dollars  pay- 
able in  12  months,  discount  at  G  per  cent,  per  annum,  because 
the  100  dollars  received  would,  if  put  to  interest,  regain  the 
6  dollars  discount. 

Rule.  As  100  dollars,  with  the  interest  for  the  given  time, 
is  to  100,  so  is  the  given  sum  to  the  present  worth,  and  the 
difference  between  the  present  worth  and  the  given  sum  is  the 
discount. 

Examples. 

1 .  What  is  the  present  worth  of  450  dols.  due  in  6  months^ 
discount  at  6  per  cent,  per  annum  ? 

6w.  I     6 

3 
100 

103  :  100  : :  450 

Ans.  435  dols.  89  cts.. 

2.  How  much  is  the  discount  of  £.308  1 3s.  due  in  18  months,^ 
at  8  per  cent,  per  annum  ?  Ans.  £.33   1  7f 

3.  What  is  the  present  worth  of  5  150  dols.  due  in  4.J  months, 
discounting^  at  the  rate  of  8  per  cent,  per  annum,,  and  allowing 
1  per  cent,  for  prompt  payment  ?  Ans.  4^50  dols. 

4.  A  is  to  pay  5927  dols.  on  the  19th  of  April,  1799,  and 
59^9  dols.  the  19th  of  July  following — It  is  required  to  know 
hyw  much  money  will  discharge  both  sums  on  the  19th  of  Jan- 
uary, 1799?  discounting  at  8  per  cent,  per  annum  ? 

Ans.  II5G9  dols.  43  cts. 

Though  the  discount  found  by  the  precedmg  method  is  thought  to  be  the 
simi  that  should  be  deducted  for  present  payment  in  justice  to  both  purlie*^, 
j.et  in.  business  the  iuiercst  for  the  time  is  taiigu  for  the  discouut.. 


12M  DISCOUNT. 

Examples. 

5.  What  ready  money  will  discharge  a  note  of  150  dollars,, 
due  in  60  days,  allowing  legal  interest,  or  6*  per  cent,  per  an* 
num  as  discount  ? 

150 

1  zzhalf  the  months. 


1,50 


150  the  debt. 
1,50  the  interest. 


14-8,50  Ans.  148  dols.  50  cts. 

6.  Bought  goods  to  the  amount  of  95^  dollai*s,  at  .90  days 
eredit,  what  ready  money  will  discharge  it,  allowing  the  inter- 
est for  the  time  at  6  per  cent,  per  annum  as  discount  ? 

Ans.  9^5  dols.  75  cts.  if  calculated  for  3  months. 
935  dols.  95  cts.  if  calculated  for  90  days. 

When  the  interest  fi)r  the  time  is  allowed  as  discoiwif,  it  is  presumed  that 
neither  party  suffers  any  loss,  but  the  following  statement  evinces  the  contrary. 

A  owes  B  100  dollars  payable  in  12  months,  for  present  pay- 
ment of  which  B  allows  6  dollars  or  the  interest  for  the  time,  . 
and  receives  9^  dollars  ;  this  sum  he  immediately  lends  to  C 
for  the  same  space  of  time,  and  then  receives  the  amount,  be- 
ing 99  doUars  6'4  cents,  which  is  36  cents  less  than  he  would 
have  to  receive  from  A,  had  he  left  the  money  in  his  hands — 
but  if  he  had  allowed  A  the  discount,  and  not  the  interest,  for 
the  time,  he  would  have  received  from  him  94  dols.^  34  cents, 
and  this  sum  being  put  to  interest,  would  amount  to  100  dolso . 
in  one  year,  which  shews  that  the  discount  and  not  the  interuiit, 
is  the  just  deduction  for  prompt  payment. 

Bat  wlicn  discouHt  is  to  be  made  for  present  payment,  without  any  regard 
to  tiiucj  tke  uitcrest  ot  the  suia,  as  calculated  for  a  year,  i.',  liie  discoujnt,  . 


DISCOUNT.  123 

Examples. 

7.  How  much  is  the  discount  of  853  dols.  at  2  percent.  ? 
853 


dols,  17,00 

Ans>   l7dol..  6cts. 

8.  How  much  money  is  to  be  received  lor  98.5  dols.  76  cts. 
discounting  4  per  cent.  ?  Ans.  i)-i6  dols.  32  ct*. 


BANK    DISCOUNT. 

The  method  used  among  hankers,  in  discounting  notes,  &c. 
is,  to  iind  the  interest  of  the  sum,  iVom  the  date  of  the  note  to 
the  time  when  it  becomes  due,  including  the  days  of  grace  ; 
the  interest  thus  found  is  reckoned  the  discount.  Thus,  if  a 
note  for  IGO  dollars,  dated  the  2d  September,  be  discounted  at 
a  bank  for  30  days,  the  interest  of  that  sum  for  33  days  being 
55  cents,  is  deducted  for  discount.  It  may  be  asked,  why  in- 
terest for  33  days  is  calculated  on  a  note  for  30,  the  answer  is, 
that  as  custom  has  allowed  the  borrower  three  days  of  grace — ■ 
that  is,  though  the  time  of  the  note  expires  on  the  first  of  Octo- 
ber (the  day  of  the  date  being  included  in  the  30  days)  he  may 
withhold  the  payment  till  the  4th — it  is  therefore  reasonable 
that  he  should  pay  interest  for  it. 

If  a  note  of  100  dollars  were  discounted  at  a  bank  for  ^0 
days,  the  interest  of  that  sum  for  63  days,  being  105  cents, 
would  be  deducted  for  the  same  reason. 

In  case  payment  of  a  note  be  not  convenient  at  the  proper 
time  a  new  note  must  be  presented  on  the  day  of  discount,  im- 
mediately preceding  the  expiration  of  the  time,  paying  the  same 
discount  or  interest  for  the  time,  as  before  stated.  Thus,  a 
note  of  100  dollars,  dated  October  7th,  1800,  for  30  days, 
though  it  is  not  payable  till  November  8th,  yet  must  be  re- 
placed by  a  new  note  on  Tuesday,  November  4th,  paying  at 
the  same  time  55  cents.  A  note  of  the  same  date,  for  100  dols. 
for  ()0  days,  though  not  payable  till  Monday,  December  8th, 
(including  in  this  time  the  days  of  grace)  must  be  replaced  by 
a  new  note  on  Tuesday,  December  2d,  paying  likewise  105 
cents.     In  the  former  case  the  borrower  sustains  a  loss  of  5 


rja  DISCOUNT. 

days  in  30,  and  in  the  latter  7  days  in  CO  by  re n (•win i^.  Al^ 
Banks  have  their  stated  times  of  discount,  generally  once  in  a 
week.  In  the  preceding  cases,  the  Bank  is  supposed  to  dis- 
count on  Tuesday.  Some  Banks  discount  twice  a  week — others- 
oftener. 

The  discount  of  any  sum,  discounted  for  30  or  60  days,  is 
found  by  multiplying  it  by  one  sixth  of  the  days.  [See  iiUeresty 
page  110.] 

Examples. 


1.    How  much  is  the  interest 

5.    What  is  the  interest  of 

of  2oS  dols.   discounted   for  30 

564:  dols.  dibcouuted  for  6"0^ 

days  ? 

days  ? 

238 

56'4 

,5  J  iz^  of  33  days. 

l,0|  =  J-of63days. 

1190 

564^0 

119 

282 

1,30,9-  5,92,2 

Ans.  1  dol.  30  cts.  9  m..  Ans.  5  dols.  92  cts.  2  ms.. 

What  is  the  discount  of  the  following  sums,  viz. 

doh.  doh.cts.msi. 

5.  159  discounted  for  30  days.  Ans.  0  87   4- 

4.  273  '-* do. 1  50   1 

5.  ()S3 do. 3  75  6 

6.  7^9 do. 4  33  9 

7.  2194 do, 12  06  7 

8.  219  discounted  for  60  days.  Ans.  2  29  9 

9.  187 do. 1  96  3 

10.  319 do. 3  34  9 

n.  6.58 do. ()  90  9 

12,       216*9 do. 22  77  4 


tS.     How 


DISCOUNT.  131 


1:3.  How  much  is  the  discount  of  a  debenture  of  319  dols. 
payable  in  210  days,  di'jcounting  for  30  days. 

Note.  28  days  are  allowed  for  a  month,  interest  being  calculated  as  if 
the  note  were  renewable. 


28)210( 
196 

[7  mo. 

319 
,5|  — J  of  33  days. 

1^ 

days. 

159  5 
15  9 

14  d. 

1 

1,75,4  for  1  mmitlu 

7 

12,27,8  for  7  months. 
mo.     877 

13,15,5 

Ans.  r3'dols.  15cts.  5  m. 

14.  What  is  the  discount  of  the  above  sum,  discounting  for 
60  days  ? 

Note.  As  notes  are  renewable  in  56  days,  the  interest  of  all  securitie*  is 
calculated  accordingly. 


56)210(3  disc 
168 

42  days. 

:ount  1 

28  d. 
14 

nor 
i 

iths. 
mo. 

319 
1,0J=:1  of  63  days. 

3190 
159 

3,34,9  for  1  discount  mo, 
3 

10,04,7  for  3  ditto. 
1,67,4 
83,7 

12,55,8 
Ans.  12  dols.  55  cts.  8  m. 

The  preceding  examples  shew  the  difference  between  dis* 
counting  for  30  and  60  days. 


132  DISCOUNT. 

What  is  the  discount  of  the  followin;^  sums,   discounting  for 
30  days  ?  *" 

dols.  days.  dols.  cts.  m$. 

15.         ]87  for    79                                       Ans.  2  i)0  0 
16\         219 115 4  C;4.  5 

17.  658.-..  47 6     74 

18.  2169. ...128 54  53  2 

What  is  the  discount  of  the  following-  sums,  discounting  for 
60  days  ? 

dnls.  days.  dols.  cts.  ms. 

19.  187  for  79  Ans.  2  7^  8 

20.  219.... 115  4  72  2 

21.  658....  47  5  79  8 

22.  2169 128  52  54. 

When  a  note  is  offered  at  a  bank  for  discount,  two  endorsers  are  generally 
required^  to  the  first  of  whom  it  is  said  to  be  payable  :  Thus — A  having  occa- 
sion for  a  sum  of  money,  procures  B  and  C  as  endorsers  to  liis  note,  and  of- 
fers it  for  discount  in  the  following  form. 

1 00  Dollars.  , 

Tor  Taliie  received,  I  promise  to  pay  B,  or  order,  of  the 

Bank,  on  demand ,  one  hundred  dollars,  xvith  interest  ajter 

^ays.  A, 

When  state  notes,  bank  shares>  &c.  are  lodged  in  a  bank  as  security  for  mo- 
nies a  note  is  presented  in  this  form  . 

For  value  received,  I  promise  to  pay  the  President,  Directors 

and  Company  of  the Bank,  or  their  order,  at  said  Bank,  on 

demand, dollars,  with  interest  aJter days,       C.  D. 


EQUATION  OF  PAYMENTS. 

The  design  of  this  Rule  is  to  find  a  mean  time  for  the  pa}'- 
tlionT  of  several  sums  due  at   different  limes. 

Rule.  INIidtiply  each  sum  by  itb  time,  and  divide  tlie  sum 
of  the  products  by  the  whole  debt;  the  quotient  is  accounted 
the  mean  time. 


i::quation  op  payments.  153 

Examples. 

1.  A  owes  B  200  dols.  whereof  40  dols.  is  to  be  pmd  in  3 
months,  6'0  dols.  in  5  months,  and  the  remainder  in  10  monthli 
«,t  what  time  may  the  whole  be  paid  without  any  injubtice  to 
either  ?  dois,      mo, 

40    X    3~    120 

60    X    5r=   300 

100    XlOiirlOOO 


200         500)1420 


Ans.  7  months  and  3  da}^, 

2.  A  is  indebted  to  B  .£.120,  whereof  one  half  is  to  be  paid 
'in  3  laonlhs,  one  quarter  in  6  months,  and  the  remainder  in  9 
months,  what  is  the  equated  time  for  the  payment  of  th-evvhoiet 

Ans.   5  months  and  7|  days. 

3.  C  owes  D  1400  dols.  to  be  pa4d  in  3  months,  but  I)  being 
in  want  of  money,  C  pays  hini,  at  the  expiration  of  2  months:, 
1000  dols.  how  much  longer  than  3  months  ought  C,  in  equity, 
to  defer  the  payment  of  the  rest  ?  Ans.  2|  months. 

Tliose  who  are  exact  in  these  calcul-dtions,  find  the  present  wt)rlh  of  each 
particular  sura,  then  find  on  what  time  these  preseirt  worths  will  be  increased 
to  the  total  of  tlic  particular  sums  payable  at  the  particular  times  to  come; 
and  that  is  the  true  equated  time  for  the  payment  of  the  wli^jle. 


BARTER 

Is  the  exchtingingof  one  commodity  for  another  on  such  terras 
as  may  be  agreed  on. 

l!lxAMPLr.S. 

1.  How  many  quintals  of  fish,  at  2  dols.^7cr  quintal,  will  pay 
iov  140  hhds.  of  aalt,  at  4  dols.  70  cts.  per  \\ki\,  ? 

140 
4,70 


<:soo 
:/6o 


d»h.        qtl. 


If    2    :     1       :  :      (;5S,00  the  ^.mount  of  the  salt. 

An«.  329  quinteJ-i, 
U 


234  BARTER.     . 

Q.  A  biws  of  B  4-  libels,  of"  rum  containing  410  gallons,  at 
1  (lol.  JJ  cts.  jier  gallon  ;  and  253  lb.  of  coffee,  r.t  21  cts.  per 
3b.  in  part  of  which  he  pays  21  dollars  in  cash,  and  the  balance 
in  boards,  at  4  dols.  per  thousand  ;  how  many  feet  of  boards 
<!id  the  balance  require  ?  •  Ans.  \27957h  feet., 

3.  B  has  C's  note  for  250  dols.  ^vith  6  months  interest  due 
on  it,  and  to  redeem  it  C  delivers  him  60  bushels  of  w  heat  at 
7.S.  6(1.  per  bushel,  50  bushels  of  corn  at  5s,  3d,  y.Qv  bushel, 
and  the  balance  in  staves  at  30 dols.  per  thousand  ;  what  num- 
ber of  staves  did  B  receive  ? 

Ans.  5550  staves,  or  4  m.  6  hun.  and  10  casts. 

4.  B  bought  of  D  the  hull  of  a  schooner  of  70  tons,  at  l6 
ilols.  per  ton,  and  paid  him  in  cash  500  dols.  3  hhds.  of  molas- 
ses containing  350gallons,  at  6'4  cts.  and  is  to  pay  the  balance 
in  New-England  rum  at  74  cts.  per  gallon  ;  how  many  gallons 
is  D  to  receive  ?  Ans.   535 /^  gals. 

5.  A  buys  of  B  250  quintals  of  fish,  at  ^5s,  per  quintal  ;  in 
payment  B  takes  100  dols.  in  cash,  2  hhds.  of  molasses  con- 
laining  87  and  92  gals,  at  3^.  Sd.  per  gallon,  1  pipe  of  brandy 
containing  120  gals,  at  7s.  6d.  per  gallon,  and  gives  3  months 
credit  for  the  remainder  ;  required  the  balance  due,  and  what 
cash  vvould  pay  it,  allowing  the  interest  of  it  for  the  time  at  6 
per  cent.  ])er  annum,  as  discount  for  prompt  payment  ? 

Ans.  Balance  is  ()82  dols.  27  cts.  6ms. —672,04,2  in  cash. 

6.  C  sells  to  D  28,674  feet  of  boards  at  8  dols.  50  cts.  per 
tiiousand,  and  takes  in  payment  J  cash,  4  barrels  N.  E.  rum 
containing  128  gallons  at  7S  cts.  per  gallon,  1  barrel  of  sugar 
%veighing  neat  2  cwt.  2  qrs.  4  lb.  at  10  dollars  per  cwt.  and  the 
Lalance  in  cofi'ee  at  25  ct?.  per  lb.  ;  how  much  money  and 
coffee  is  C  to  receive  ? 

Ans.  81  dols.  24  cts.  3  ms.  and  1^9.^^%  lb.  of  coffee. 

7.  C  has  nutmegs  worth  7s,  6d,  per  lb.  in  ready  money, 
l>ut  in  barter  he  will  have  8.9. ;  I)  has  tobacco  worth  9d.  per  lb. ; 
1k)v»  much  must  he  rate  it  per  lb.  that  his  profit  may  be  ecjual 
to  C's  ?  Ans.  Old. 

8.  A  has  tea  which  he  barters  with  B  at  lOd.  per  lb.  more 
than  it  cost  him,  against  cam.brick  which  stands  B  in  10-5.  })er 
yard,  but  he  puts  it  at  125.  6d.  ;  I  would  know  the  first  cost  of* 
llie  {c'd  ?  Ans.  3.9.  4f/.  per  lb. 

"-  A  h:'^-  240  buslicls  of  rye,  which  cost  him  90  cts.  per 
i.c  bartei-s  with  B  at  95  cts.  for  wheat  that  stands 
^  or  buelicl ;   iiow   many  buchels  of  v;hcat  is  he  t« 


LOSS  AND  GAIN.  135 

Tfccive  in  barter,  find  at  what  price  is  it  to  bo  rated,  that  their 
gains  may  be  equal  ? 

Ans.  21S  ro^c>  bushels,  at  104  J  cts.  per  bushel. 

10.  A  and  B  barter  some  goods — A  put  his  at  30.^,  shil- 
linnrs,  and  gains  8  per  cent.  B  puts  his  at  24- ^-^^j  shillings,  and 
gains  at  the  same  rate  ;  what  was  the  first  cost  of  the  goods  ? 

Ans.  28c«f.  and  2'^?.  6V.  ' 

11.  A  and  B  barter  ;  A  has  cloth  that  cost  28r/.  B's  cost 
liini  22^.  and  he  puts  it  at  Q5cl.  ;  how  high  must  A  put  liis  to 
gain  10  per  cent,  more  than  B  ?  Ans.  3o(J. 

12.  C  and  D  barter — C  makes  of  7s.  6s,  S(L  D  makes  of 
7^.  6c/.  Ja.  3c!»;  who  has  lost  most,  ajul  by  how  mucli  per  cent,  f 

Ans.  C  loses  if-  per  cent,  more  than  D. 


LOSS  AND  GAIN 

Is  a  rule  that  discovers  what  is  gained  or  lost  in  buying  or 
selling  goods,  and  instructs  merchants  and  traders  to  raise  or 
iall  the  price  of  their  goods  so  as  to  gain  or  lose  so  much  per 
cent.  &c. 

EXA^VIPLES. 

1.  Bought  a  piece  of  broadcloth  containing  53  yards,  at  4 
dols.  Go  cts.  per  yard,  and  sold  at  5  dots,  per  yard  ;  what  is  tkc 
profit  on  the  whole  ? 

5 

4,65 

yd,         yd'^^ 

If     1     :     ^35    ::    53 
35 

26\5 
159 

18,55      Ans.   18  dob.  55  cts 

2.  If  1  lb.  of  coffee  cost  28  cts.  and  is  sold  for  31  cts.  what 
is  the  profit  on  3  bags,  weighing  293  lbs.  neat  ^ 

Ans.  8  dols.  79  cts. 


>3^  LOSS  AND  GAIN.. 

o.  Bought  Ji  piece  of  baize  of  42  yards,  for  £A  14  6\  anA 
sold  it  at  2*,  6d.  per  yard;  wiiat  is  the  gain  or  loss  on  the  whole 
pit'ce  ?  Ans.   10^.  6c?.  gain. 

4.  A  merchant  bought  59  cwt.  3  qr.  14  lb.  of  iron,  at  \l% 
dols.  per  ton,  paid  freight  and  charges,  24  dols.  what  is  the 
£Liin  or  loss,  if  he  sells  the  whole  at  37s,  ^d,  per  cwt.  ? 

Ans.   13  dols.  26"  cts.  gain. 

5.  If  a  gallon  of  wine  cost  6s.  8d,  and  is  sold  for  7s.  Qd^ 
yvh'dt  is  tile  gain  per  cent.  ? 

7     2 
6     8 

s.  d. £, 

li'    6  8        :         6    :  :     100         Ans.  7 J  per  cent,  gain* 

6.  When  20  per  cent,  loss  is  made  on  coflee,  sold  at  20  cts^ 
per  lb.  what  was  the  first  cost  ?  Ans.  25  cts. 

7.  At  13^  cts.  profit  on  the  dollar,  how  much  is  it  per  cent.  ^ 

Ans.   13j  per  cent,  or  13  dols.  50  cts.  per  100  dols. 

8..  A  trader  sells  his  goods  at  2jrf..  profit  on  the  shilling, 
iow  much  is  it  per  cent.  ?  Ans.  20f ,  or  ^.20  l6  8 

9.  Which  is  the  better  bargain,  iri  purchasing  fis?i^  1'7  shil- 
lings per  quintal,  and  4  months  credit,  or  Kis.  Sd,  cash  ? 

Ans.   TJu^  are  alike. 

Pkoof.  The  present  worth  of  175.  found  by  disGonnt,  is  equal  to  163.  8d. 
and  1G.>;.  '6(L  \%i:h  4  months  interest,  will  amount  to  17.5. 

iO.  A  bought  a  piece  of  shalloon,  containing  34  yards,  at' 
3.V.  4f/.  per  yard,  and  sold  it  at  12^  per  cent,  loss,  iiow  muck 
•iid  he  sell  it  per  yard  ?  Ans.  2s,  lid. 

11.  Bought  rum  at  f)^  cts.  per  gallon,  at  what  rate  must  it. 
l?e  sold  to  gain  20  per  cent.  ?  Ans.  lOS  cents. 

12.  A  trader  bought  1  hhd.  of  rum,  of  a  certain  proof,  con- 
taining 115  gallons,  at  1  dol.  10  cts.  per  galhm,  how  many 
i^allons  of  water  n^ust  l\c  put  into  it  togain5  dollars,  by  selling 
it  at  1  dollar  per  gallon  ?  Ans.  16.^  gallons. 

13.  Bought  4  hhds.  of  rum,  containing  450  gallons,  at  1  dol. 
per  gallon,  and  sold  it  at  1  dol.  20  cts.  per  gallon,  and  gave  3 
months  credit  ;  now  allowing  the  leakage  of  the  rum  while  in 
n^.y  possession  to  be  10  gallons,  I  would  know  the  gain  or  loss, 
<liscounting  for  the  present  worth  of  the  debt  at  6  per  cent^ 
j>er  annum  ?  Ans,  70  doh,  IJ)  Cts.  gain. 


LOSS  AND  GAIN.  137 

14.  A  vintner  buys '595 gallons  of  wine,  at  Gs,  3(1  pergallon, 
in  ready  money,  and  sells  it  immediately  at  Gs.  ^d.  per  gallon, 
payable  in  3  months,  how  much  is  his  gain  or  loss,  supposing  he 
allows  the  interest  for  the  time,  at  6'  per  cent,  per  annum,  as 
discount  for  present  payment  ?  Ans.  £.11    17   8  gained, 

15.  What  would  be  the  gain  or  loss  on  the  aforesaid  wine, 
supposing  the  discount  for  present  payment  to  be  made  at  2per 
cent,  without  any  regard  to  time  ?      Ans.  .£.10   1/    6^  gain. 

l6'.  A  merchant  bought  a  parcel  of  cloth  at  the  rate  of  1  doU 
fur  every  2  yds;  of  which  he  sold  a  certain  quantity  at  the  rate 
of  3  dols.  for  every  5  yds.  and  then  found  he  had  gained  asmucji 
as  18  yards  cost,  how  many  yards  did  he  sell  t       Ai^.s.  ^0  yds. 

17.  Bought  rum  at  1  dol.  25  cts.  per  gallon,  which  not  prov- 
ing so  good  as  I  expected,  I  am  content  to  lose  18  per  cent,  by 
it,  how  must  I  sell  it  per  gallon  ?  Ans.    1  dol.  2-2  cts. 

1  8.  II  sells  a  quantity  of  corn  at  T  dollar  a  bushel,  and  gains 
20  per  cent,  some  time  after  he  sold  of  the  same,  to  the  amount 
of  37  dois.  jO  cts.  and  gained  50  per  ceiU.  how  many  bubhels 
>^ere  there  in  the  last  parcel,  and  at  what  rate  did  he  sell  it  per 
bushel  ?  An>^.  30  bushels^  at  I  doL  25  cts.  per  bushel. 

19.  A  distiller  is  about  pu releasing  10000  gallons  of  molasses, 
which  he  can  have  at  48  cents  per  gallon,  in  ready  money,  or 
50  cen1s  with  two  months  credit,  it  is  required  to  know  which  is 
more  advantageous  to  him,  cither  to  buy  it  on. credit,  or  to 
borrow  the  cioney  at  8  per  cent,  per  anoum  to  pay  the  ca^li 
price  ^  Ans.  He  will  gain  13G  dols.  by  paying  thciCash, 

20.  A  tobacroTiisi'^t)ti^-s  4-^hocrchea'ds  of' to^f.^'^co  ucigM 
38  cwt.  2  qrs.  8  lb.  gj^osij  tai'e  '^4^  Ib/'per  hhd:  'at  * ^5)' lI 61  •?por 
cwt.  ready  money,  ail  ({  J>dl^  it  at  11  Jr/.  per  fb.  allo<\'}ti^g' tare  at 
1 4- lb.  per  cwt.  to  rc^ccive  two-thirds  in  cash,  and  for  the  rc~ 
n^iiindcr  a  note  at  ^0  days  credit  ;  his  gain  or  loss  js  required, 
suppe>sing  the  note  is  discounted  at  a  bank  where  discouiit  is 
made  for  60  days.  Ans.  283  dois.  43  cts.  caiu,. 


M2 


138  ALLIGxXTION  MEDIAL. 

A  LLIGATION  MEDIAL 

Is  when  iao^  quantities  and  prices  of  several  things  are  given^ 
to  find  the  mean  price  of  the  rnixture  compounded  of  those 
things. 

RuLK.  As  the  sum  of  the  quantities  or  whole  composition 
is  to  their  total  value,,  so  is  any  part  of  the  composition  to  its 
mean  price. 

Examples, 

1.  A  grocer  would  mix  25  lb.  of  raisins,  at  8  cents  per  lb. 
«ncl  35  11).  at  10  c^nts  per  lb.  with  40  lb.  at  1.2  cents  ^3er  lb. — ■ 
>vhat  is  1  lb.  of  this  mixture  worth  ? 

//.'.  cts,  cts. 

2.3  at         8    200- 

35    10 350 

40    12    ....    480 


100  103a 

Ih.  cts.  lb. 

If     100        :        1030  :  :      1 
1 


llG0)10i3O 

els,     10,3  Ans.   10  cents,. 3  mills. 

2.  A  goldsmith  mixes  8  lb.  og  oz.  of  gold,  of  14  carats  fine^ 
with  121b.  S^oz.  of  18  carats  fine  ;  what  is  the  fineness  of  this^ 
mixture  ?  Ans.    lO^W  carats. 

3.  A  grocer  would  mix  12  cwt.  of  sugar,  at  10  dols.  percwt. 
with  3  (w.t.  .at  8f  dols.  per  cwt.  and  a  cwt.  at  7  J  dols.  per  cwt. 
what  will  5  cwt.  of  this  mixture  be  worth  } 

Ans.  44  dob.  78  cts.  2  ms. 

4.  A  refiner  melts  2g  lb.  of  gold^  of  20  carats  fine,   with  4 
lb.  of  18  carats  fine;  how  much  alloy  m.ust  he  put  to  it  to  make' 
it  22  carats  fine  ?        Ans.   It  is  not  fine  enough  by  3  c:,  carats, 
M)  that  no  alloy  must  be  })ut  to  it,  but  more  gold. 

!).  A  nialster  mingles  30  quarters  of  brown  mult,  at  28,?. 
per  cjuartcr,  with  4()  quarters  oi'  pale,  at  30a\  per  quarter,  and 
Vi'  (uiartcrs  of  high  dried  ditto,  at  25^.  per  quarter;  \Aliat  is 
i!:o  .;iiuc  oi'  tj  bushels  of  thiii mixture  ?     Ans.  ^'.1   86.  2it^.| 


ALLIGATION  MEDIAL.  13^ 

6.  If  I  mix  27  bushch  of  wheat,  at  5s,  6d.  the  bushel,  with 
the  same  quantity  of  rye,  at  4-5.  per  bushel,  and  14  bushels  of 
barley,  at  2s.  8d.  per  bushel,  what  is  the  worth  of  a  busliel  of 
this  mixture  ?  Ans.  4^.  3|(i.f  § 

7.  A  grocer  mingled  3  cwt.  of  sugar,  at  56s.  per  cwt,  6 
cwt.  at  c£.  1  17  4-  per  cwt.  and  3  cwt.  at  £,3  14  8  per  cwt, 
what  is  1  cwt.  of  this  mixture  worth  ?  Ans.  £.2   114 

8.  A  mealman  has  flour  of  several  sorts,  and  would  mix  3 
bushels  at  3^.  5d.  per  bushel,  4  bushels  at  5s..6d.  per  bushel, 
and  5  bushels  at  4a\  Sd.  per  bushel,,  what  is  the  worth  of  a 
bushel  of  this  mixture  ?  ^  Ans.  4<s.  J^d,  ^^     > 

9.  A  vintner  mixes  20  gallons  of  Port,  at  5s.  4:d.  per  gal- 
Ion,  with  12  gallons  of  White  wine,  at  5s.  per  gallon,  30  gallons 
of  Lisbon,  at  6s,  per  gallon,  and  20- gallons  of  Mountain,  at 
4-^.  6d.  per  gallon,  what  is  a  gallon  of  this  mixture  worth  ? 

Ans.  5*.  33^.  If 

10.  A  farmer  mingled  20  bushels  of  wheat,  at  5s.  per  bush* 
fl,  and  36  bushels  of  rye,  at  3^,  per  bushel,  with  40  bushels  of 
barley,  at  2s.  per  bushel,  I  desire  to  know  the  worth  of  a  buslw 
el  of  this  mixture  ?  Ans.  3  shillings. 

11.  A  person  mixing  a  quantity  of  oats,  at  25.  6f/.  per 
bushel,  with  the  like  quantity  of  beans,  at  'is.  6d,  per  bushel,. 
"Would  be  glad  to  know  thq  value  of  1  bushel  of  that  mixture  ? 

Ans.  3s.  6d, 

12.  A  refmer  having  12  lb.  of  silver  bullion  o£  6  oz.  fine,, 
would  melt  it  with  8  lb.  of  7  oz.  fine,  and  10  lb.  of  8  oz.  fine,, 
required  the  fineness  of  1  lb.  of  that  mixture  ? 

Ans.  O'oz.  ISdwt;  l()grs, 

13.  If  with  40  bushels  of  corn,  at  4a'.  per  bushel,  there  are 
mixed' 10  bushels,  at  6s.  per  bushel,  30  bushels,  at  5s.  per 
bushel,  and  20  bushels,  at  3^.  per  bushel,  what  will  10  bushels 
of  that  mixture  be  worth  }  Ans.  £.2  3s..  ' 


ALLIGATION  ALTERNATE 

Is  the  method  of  finding  what  quantity  of  any  number  of 
simples,  whose  rates  are  given,  will  compose  a  mixture  of  a 
givrn  rate  ;  so  that  it  is  the  reverse  of  Aiiigiition  Medial,  aiid 
ftuiy  be  proved   by  it. 


U0 


ALLIGATION  ALTERNATE. 


Rule.  L  Write  the  rates  of  the  simples  in  a  column  tin- 
der each  other. 

2.  Connect  or  link  with  a  continued  line  the  rate  of  each 
simple  which  is  less  than  that  of  the  compound,  with  one,  or 
any  number,  of  those  that  are  greater  than  the  compound,  and 
each  greater  rate  with  one  or  any  number  of  the  less. 

3.  Write  the  difierence  between  the  mixture  rate  and  that  of 
each  of  the  simples,  opposite  the  rates  with  which  they  are 
linked. 

4.  Then  if  only  one  ditfcrcncc  stand  against  any  rate,  it  will 
be  the  quantity  belonging  to  that  rate  ;  but  if  there  be  several 
their  sum  will  be  the  quantity.. 

Examples. 


1.  A  merchant  would  mix  wines  at  14.9.  ipv.  t5s.  and  S'?^?. 
per  gallon,  so  that  the  mixture  may  be  worth  185.  the  gallon  j 
ivhat  quantity  of  each  must  be  taken  ? 


'"l 


ip- 

22- 


4 

at 

14.9. 

1  at 

]  ,3.9. 

3  at 

]  ri.v. 

.  4  at 

'22.S, 

Or  thus 

l-f4 

5  at 

M.9.. 

I 

1  at 

1  5.V. 

44-3 

7  at 

1Q9.. 

4 

4  at 

226.. 

NoTF.  Questions  in  this  rale  adnnt  of  a  great  variety  of  answers^  accord- 
irig  to  the  manner  of  hnking  tlieni. 

2.     How  much    wine,  at  6s.    per   gaRon,  .and  at  4^.   per 

gallon,  must  be  mixed  together,  that  the   composition  may   be 
worth  06'.  per  gallon  ?  Ans.  1  qt.  or  1  gal,  of  each,  &c. 

.3.  How  much  corn,  at  Qs.  6cL  3v.  Sd.  4^.  and  4.9.  8(A  ]^or 
hushel,  mu'^i  be  mixed  together,  that  the  compound  riuiy  be 
woilh  3*.  lOd.  per  bushel  ? 

Ans.  12  at  2s.  6d.  19  at  '^s.  Sd.  10  at  4s.  and  IC  at  4s.  M. 

4.     A  goldsmith  lias  gold  (,f  17,    IS,  22  and  ?4  carats  fine- 
]row  much  must  be  tale  of  each  lo  m;ike  it  21  carats  fine  ^ 
AiUi    3  of  17,  1  of  18,  3  of  22,  aari  i  of  '^4& 


ALLIGATION  ALTERNATC. 


Ul 


5.  It  is  required  to  mix  brandy  at  8.9.  wine  at  7^»  cidor  afc 
l5.  and  water  together,  so  that  the  mixture  may  be  worth  5<s\ 
per  gallon  } 

Ans.  9  gals,  of  brandy,  9  of  wine,  5  of  cider,  and  5  of  water. 

JFken  the  whole  composition  is  limited  to  a  certain  quantitij. 

Rule.  Find  an  answer  as  before  by  linking  ;  then  say,  As. 
the  sum  of  the  quantities,  or  differences  thus  determiae^i,  is  to 
the  given  quantity,  so  is  each  ingredient,  found  by  liuking,  t^ 
the  required  quantity  of  each. 

Examples, 

6.  How  many  gallons  of  water  must  be  mixed  with  wine 
worth  3.V.  per  gallon,  so  as  to  fill  a  vessel  of  100  g^allons,  anit 
that  a  ge^Uon  may  be  afforded  at  2s.  6d,  ? 

r    0 6 

)) 
|S5- 


30  < 


30 


36 


100 
6 


36)600(16 
36 


:  100  :: 
SO 

36)3000(83 
288 


3# 


240 
216 


120 

108 


54^  12 

Ans,  8i>}  gallons  of  wine,  and  l6f  of  water. 

7.  A  grocer  has  currants  at  4^.  6cL  9(L  and  ild.  per  Ib^ 
and  he  would  make  a  mixture  of  240  lb.  so  that  it  might  bo 
atlbrded  at  8^.  per  lb.  how  much  of  each  sort  must  he  take? 

Am.  72  lb.  at  4tf.  24  at  6d.  48  at  9d.  and  9d  at  11(/. 

8.  IIow  much  gold  of  15,  of  17,  of  18,  and  of  22  carats, 
fme,  must  be  mixed  together,  to  form  a  composition  of  40  oz^ 
of  20  carets  fine  ? 

\ni.  5  oz^  of  15,  of  17,  and  of  18,  and  25  oz.  cf  2!^,> 


14^  ALLIGATION  ALTERNATE. 

JJlien  one  of  the  wgrecUents  is  limited  to  a  certain  quantify. 

Rule.  Take  the  clifTcrence  between  each  price  and  the 
mean  rate,  as  before ;  theii. 

As  the  difference  of  that  simple,  whose  quantity  is  given,  is 
to  the  rest  of  the  differences  severally,  so  is  the  quantity  given, 
to  the  several  quantities  required. 

Examples. 

9.  How  much  wine,  at  Ss.  at  5.9.  ()c/.  and  at  (7,5.  the  gallon, 
must  be  mixed  with  three  galhms,  at  4s9.  per  gallon,  so  that  the 
mixture  may  be  worth  5^.  ^d.  per  gallon  ? 


64. 


48— 



60- 

—  -^ 

66- 

) 

70 

1   4, 

JO 

:      10 

JO 

:     20 

10 

:      20 

8-f  2=1:10 

8-f2==10 

164-4=20 

16-f  4—20 


:  3  :  3 
;  3  :  6 
:      3      :     6 

Ans.  3  gallons  at  5^. ',  6  at  Ss,  6d,  and  6  at  6s, 

10.  A  ^irocer  would  mix  teas  at  12^.  10^.  and  6s.  with  20 
lb.  at  4.9.  per  lb.  ;  how  much  of  each  sort  must  he  take  to 
make  the  composition  worth  8^.  per  lb.  ? 

Ans.  201b.  al  4s.  ;  10 ib.  at  65. ;  10  lb.  at  lOs.  ;  and  20  lb.  at  125. 

11.  How  much  gold  of  15,  of  17?  iin<-l  cf  22  carats  fine, 
must  be  mixed  with  5  oz.  of  1 8  carats  fine,  so  that  the  com- 
position may  be  20  carats  fine  .? 

Ans.  5  oz.  of  15  carats  fine,  5  oz.  of  17?  and  25  of  22». 


position: 

Position  is  a  rule,  which,  by  false  or  supposed  numbers, 
taken  at  pleasure,  discovers  the  true  one  required.  It  is  divi- 
ded into  two  parts,  Single  and  Double. 

SINGLE  POSITION 

Is,  by  using  one  supposed  number,  and  working  with  it  as  the 
true  one,  you   find  tiic  real  number  required  by  the  following- 


POSITION.  14^ 

"Rule:  As  the  total  of  the  errors  is  to  the  given  sum,  so  is 
the  supposed  number  to  the  true  one  required. 

l^iiooF.  A(!d  the  several  parts  of  the  result  together,  and  if 
•it  agrees  with  the  given  sum,  it  is  right. 

Examples. 

1,  A  school-master,  being  asked  how  many  scholars  he  had, 
said,  If  I  had  as  many,  half  as  many,  and  one  quarter  as  many 
more,  I  should  hMve'26'4  ;  how  many  had  ho 

Suppose  he  had     72 

As  maiiy 72 

J  as  many ......  36 

^  as  many  •  •  •  ••  18 

As     19s     :     9.64^     :  :     72 

72 


? 


Proof. 

528  9() 

J  848  5)6 

48 


198)  19008(96  Answer.  24 ' 

1782  ■ 

264 


^.  A  person,  after  spending  J  and  J  of  his  money,  had  6& 
(dollars  lett  ;   what  had  he  at  first  ?  Ans.    144  dols. 

3.  A  certain  sum  of  money  is  to  be  divided  between  4  per- 
sons, in  such  a  manner,  that  the  first  shall  have  J  of  it,  the 
second  {,  the  third  J-,  and  the  fourth  the  len^.ainder,  which  is 
28  dollars  ;  what  was  the  sum  ?  An.';.    112  dols. 

4.  A  person  lent  his  friend  a  sum  of  money  unknown,  to 
receive  interest  for  the  s^me,  at  6  {>er  cent,  per  annum,  simple 
interest,  and  at  the  end  of  5  years  he  received  for  principal 
and  interest  044  dollars  SO  cents  ;  what  vyas  the  sum  lent  ? 

Ans.  496  dols. 


DOUBLE  POSITION 

Is,  by  making  use  of  two  supposed  nu!iibers,    v.hich,  if  both 
prove  iiilse,  are,  with  tlieir  errors,  to  be  thgti  disposed  : 

iluLE.    1.      Place  each  error  {ig'iii..st  its  lO'.nective  position. 
t.   I>IuUinlv  them  cross  vviie. 


444  •  POSITION. 

3.  If  the  errors  are  alike,  that  is,  both  greater  of  both  less 
than  tlie  given  number,  divide  the  difierence  of  the  products 
by  the  difference  of  the  errors,  and  the  quotient  is  the  ansyver : 
But  if  the  errors  be  unlike,  divide  the  sum  of  the  products  by 
the  sum  of  the  errors,  and  the  quotient  will  be  the  answer. 

Examples. 
1.     B  asked  C  how  much  his  horse  cost  ;   C  answered,  that 
if  he  cost  him  thn  t-  limes  as  much   as  he  did,    and  15  dollars 
moie,  he  would  stand  him  in  300  dollars  ;  what  was  the  price 
of  the  horse  ? 

doh,  dols, 

Suppose  he  cost  90       Suppose  he  cost  96 
S  '  3 


270  2S8 

15  15 


QS5  too  lit.  by  15  dls.     303  too  much  by  3  dls, 
90  15-- 

X 

96  3  + 


15      1440       270 
3       270 


Sum  of  the  errors  1«)    1710     (95  answer  95 

162  3 

90  15 

300  proof. 

2.  Two  p'crsons,  A  and  B,  have  both,  the  same  income  ;  A 
saves  one-lifth  of  his  yearly  :  but  R,  by  spending  150  dollars 
per  annum,  moi^  than  A,  at  tlie  Qwd  of  8  years  tinds  himself 
4-00  dollars  in  debt ;  what  is  their  iiicome,  and  what  does  each 
spend  per  annum  ? 

Ans.  Their  income  is  500  dollars  per  annum  ;  also  A  spends 
400,  and  B  5 '30  dollars  per  annum* 

3.  There  is  a  fish  whose  head  is  9  inclies  long^  and  his  tail 
is  as  long  as  his  head  ar.d  half  his  body,  and  his  body  is  as  long 
as  the  head  and  tail }  what  is  the  whole  length  of  the  fisli  ? 

Ans.  6  feet. 


POSITION.  1 15 

4.  Divide  15intohvo  such  parts,  so  tliat  ^vhcn  tlic  greater 
is  multiplied  by  4,  and  the  less  by  \6,  the  products  will  be  e- 
flual.  Ans.  12  and  3. 

6.  A  man  had  two  silver  cups  of  unequal  weight,  having  one 
cover  to  both,  5oz,  ;  now  if  the  cover  is  put  on  the  less  cup  it 
will  be  double  the  weight  of  the  greater  cup,  and  put  on  the 
greater  cup  it  will  be  three  times  as  heavyas  the  less  cup  :  what 
is  the  weight  of  each  cup  ?  Ans.  3  oz.  less — 4  oz.  greater. 

6,  A  person  being  aj^ked,  in  the  afternoon,  what  o'clock  it 
was,  answered  that  the  time  past  trom  noon  was  equal  to  ^-3  of 
the  time  to  midnight  :  required  the  time  ? 

Aus.  30  minutes  past  one. 


EXCHANGE. 

Exchange  is  the  paying  of  money  in  one  place  or  country, 
for  the  like  value  to  be  received  in  another  place  or  country. 

There  are  two  kinds  of  money,  viz.  Real,  and  Imaginary, 

Real  movetj  is  a  piece  of  metal  coined  by  the  authority  of  the 
State,  tind  current  at  a  certain  price,  by  virtue  of  the  said  au- 
thority, or  of  its  own  iatrinsic  value. 

Imaginary  money  is  a  denomination  used  to  express  a  sum  of 
mofiey  of  which  there  is  no  real  species,  as  a/ivrc  in  France,  a 
pound  in  America,  because  there  is  no  species  current,  in  this 
or  that  country,  precisely  the  value  of  either  of  the  sums. 

Tar  of  Exchange  is  the  intrinsic  value  of  the   money  of  one 
country  compared  with  that  of  another  country,  as  one  pound 
'  sterling  is  equal  to  thirty-five  shillings  Flemish. 

Course  of  exchange  is  the  current  or  running  price  of  ex- 
change, which  is  sometimes  above,  and  sometimes  below  par, 
varying  according  to  the  occurrences  of  trade,  or  demand  for 
mone)'.  Of  this  course,  there  are  tables  published  daily  in 
commercial  cities  :  thus  by  Lloyd's  List,  of  2i^\.  December, 
"^799^  tlie  course  of  exchange  between  Hamburgh  and  London, 
was  32-v.  G}id,  Flemish,  per  pound  bterling,  being  i'5.  b^d,  under 
par,  or  loss  to  London.  ^ 


U6  EXCHANGE. 

GREAT-BRITAIN. 

The  money  of  account  is  pounds,  shillings,  pence  and  far- 
things. 

The  English  Guinea  is  21  shillings,  Sterling. 

Weights  and  measures  generaljy  as  in  the  United  States, 

The  United  States  dollar  is  equal  to  4*.  6d,  Sterling. 

To  Change  Sterling  to  Federal  money. 

Rule.  Annex  three  cyphers  to  the  sum  (if  pounds  only) 
and  multiply  itby  4  ;  this  product  divide  by  9>  andyou  have  the 
answer  in  cents.  11  there  be  shillings,  &c.  the  usual  method 
is  to  reduce  it  to  Massachusetts  money,  by  adding  one  third  to 
it,  and  then  reduce  this  sum  to  Federal. 

Examples. 

1.  Change  .£.48  Sterling  to  Federal. 

48000 
4 

9)192000 

21333J  cents.  Ans.  213  dols.  33§  cts. 

2.  Change  £.389  17  4J;SterlingtoFederal,exchangeat33j 
per  cent,    that  is,   £.133j    INIassachusetts  for  £.100  Sterling. 

J)389   17  4J  Sterling 
129   19   1|  Exchange 

519  16*  6     Massachusetts 


,3)519,825 


Cts.  173275  Federal.  Ans.  1732  dols.  75cts» 

Note.     Sterlini::  is  cbanscd  to  Massaclmsclls  money  by  adding   one-third 
to  the  suiW;  and  MassachubcUs  lo  Sterling  by  deducting  ouc-lbi5rtli  Irom  it. 


To  change  Federal  Cnrrenci/  to  Sterling, 
PvULB.     Work  bv either  of  the  following  method?. 


EXCHANGE.  147- 


Examples. 
Chatige  1732  dollars  75  cents  to  sterluig. 


First  Method. 
1732 

4..       i 
6d.      i 
50  cents 
25  cents 

346     8 
43     6 

2 

1 

3 
1.^ 

Ans. 

£.389     17 

H 

Second  Method. 
1752,75 
,3 

5191825 
20 

16(500 
12 

6|000 
1)519  l6  6  Massachusetts 
129  19   U  Exchange 


Ans.  £.389  17  4j  Sterling. 
1,     What  is  the- Federal  amount    of  an  invoice  of  goods, 
charged  at £.196  14  6  Sterling  advancing  on  it  25  per  cent.  ? 
25    J)  196  14  6     Sterling 
49     3  7J  Advance 

245   18   ll 

Exchange  at33j  per  cent.  81   19  4^ 

£.327   17  6     Massachasctts 


3)327S75 


cts.      109291^  Ans.  1092    dols.   9lf  cts. 
2.  The  Sterling  cost  of   certain   goods    being  c£.6'0   12    6, 
what  does  it  amount  to  in  Massachusetts  money,  advancing  on 
it  50  per  cent.  ? 

60   12  6 
50  per  cent,  advance  30     6  3 

90  18  9 

Exchange  at  33  J  per  cent.  30     6  S 


Ans.    £.121      5  0  JMaisachusotts  money. 
The  mercantile  method,  with  50  per  cent,  advance,  is  to  double  the  Sterling 
for  Massachusetts  money  ;  thus, 

60  12  6  Sterling. 
2 


£.121     5  0  jMassachuietts,  as  above. 


lis  EXCHANGE. 

3,  An  invoice  of  goods,  charged  at  £.6'2  19  7  stciTingj  h 
Srold  at  75-  per  cent.  ad\ance  on  tlie  sterling  cost,  how  much 
is  it  in  ^Jassachusetts  money  ? 

52   19     7 
Advance  at  50      26     9     9 -J 
25      13     4    10| 

92    U      Si 
Exchange  at  Sol  percent.  30   18      1 

Ans.  .£.123   12     4|  JMassachiisetts  money. 

The  mercantile  method,  with  73  per  cent,  advance,  is  to  multiply'  the  ste?- 
?hig  by  2|  for  MHSsichusetts  money. 

Thus,     52   19     7 


105   19     3 
17    13     2i 


£.123   12     4|  Massachusetts  money,as  above. 
4.     The  sterling  cost  of  certain    goods  being   £.214-   11   6, 
tow  much  is  it  in  Federal  money,  advancing  thereon   60    per 
cent.  ^ 

214  11     6 


343     6     4| 
Exchange  J  114     8     9  J 


457  ^o  24  Massachusetts 

Or  thus,        214  11  6  Sterling 

Exchange  J    71  10  6 

286  2  0 

50  J      143  1  0 

10  j        28  12  2J 

457  15  2l  Massachusetts 


,3)457,759 


Dollars    1525,861  Ans.    1525  dols.  86^  cts. 


EXCHANGE.  149 

5.  What  is  the  amount  of  a  bill  of  exchange  of  £.115   14  9 
sterling,  sold  in  Boston  at  1 J  per  cent,  advance  ? 
J)  115    14     9     Sterling 
38   11     7     Exchange 


Or  thus. 


154 

6 

4     INIai 

,3)] 

154,317 
514,39 

n 

Federal 

51439' 
25719 

Cents 

Value  at 
Advance 

771 

par 

par 

pr.  c 
do. 

158 

dch.     cl3: 
514     39 
7     7li 

Amount 

522      lOj 

Value  at 

514 

cts. 

39 

Adv.  at  1 

t.    5 
2 

14   3 

57   1 

7- 

71  4  ; 

Amount  5-22   10  4. 

6.     A  merchant  in  Boston  receives  a  parcel  of  goods   from 
London,  charged  in  the  invoice    at  the   following   prices,    and 
marks  them  for  sale  at()0  percent,  advance  on  the  sterling  cost ; 
required  the  selling  price  of  each  in  Massachusetts  money  ; 
5.     d.  s.     d.  doh.   ct'f.  m, 

8  sterling,  adv.  60  per  ct.  29     d  A  Massa.  raonev,  or      4     85     3 

12     51   • 2       7     .'» 

7     jl 1     18     3 

13     Oi-v.... o     17     6 

36     3 6       4 

70     61 11     75     (7 

2     5| 41 

18  10 40     2 6     69     4 

11        23     5i ..      3     91 

2     4 4  Hi 82     3 

32     3 68     9^- 11     46     G 

27     9 50     n •  •  .  • 9     86     3'^ 

K   2  """■ ' 


13 

8: 

6 

10 

3 

4 

6 

1^ 

17 

0 

S3 

1 

1 

2 

130  EXCHANGE. 

7.  A  watcli  that  cost  15  guineas  in  London,  was  sold  in 
Boston  at  50  per  cent,  advance  on  the  sterling  cost,  \vha.t  was 
the  price  ? 

15  guineaszi:£.I5   15  0  Sterling 
2 

31   10  0  Massachusetts 

,3)31,5 

Ans.      105  dollars. 
S.     How  much  is  the  premium  of  insuring  c€.294?  at  8  guin* 
eas  per  cent.  ?  Ans,  £.24:   13   11  Sterling, 


Mercantile  methods  of  calculating^  tiz» 
At  25perct.  disc,  from  the  sterling  co>t,  multiply  it  by  1  for  the  answer  ia 
Massachusetts  money. 
10      li 

pai- H 

12|  per  ct.  adv.  on  the  sterling  cost,  multiply  it  by      ll 
2o 1| 

SIJ l| 

60 2 

m H 

65 2l 

75     4 

m 4 

100  c 2| 

125  . 3 

140  • 3i 

150  si 

162|  3f 

175  3| 

200  4 

IRELAND. 

The  money  of  account  as  in  England,  but  different  in  value. 
The  par  between  Plngland  and  Ireland  is  83  per  cent,  that  is, 
i^MOO  sterling  money  is  ^.108  6"  8  in  Ireland. 

Mercantile  weights  and  measures,  the  same  as  in  England. 
The  United  States  dollaris  equal  to  4a\  lO^^i.  Irish. 
The  English  guinea  is  equal  to  22s.  ^d.  Irish. 

To  reduce  Irish  money  to  Federal, 

IluLF,.  Reduce  the  given  sum  to  halfpence,  annex  two  cy- 
phers to  it,  and  then  divide  by  117,  (the  half  pence  in  a  dollar) 


EXCHANGE.  151 

and  the  quotient  is  the  answer  in  cents.  Or  reduce  the  Irisb 
to  Sterling,  by  deducting  ^^  trom  it,  and  then  work  as  for 
Sterling. 

ExAMPLEr 

Change  £.Q7S   15  9  'rish  money  to  Federal. 

First  method.  Serond  method'. 

578   15  9  1-3)278   U     9  Irish. 

20  21      8   II  Kxchange 


557i>  ^57     0   10  Sterling 

12  85   15     7i 


66909  345     2     5i  Mass. 

2 


9)13381800 


^3)343,122 


5X13  =  117 1143,74  cents 

13)1486866 

1 14374  cents.  Ans.  1 143  dols.  74  cts. 


To  chancre  Federal  money  to  Irish, 

m 
Rule.     Multiply  the  given  sum  by  117,  reject  two  figures 

from  the  product  to  the  right  hand,  and  the  remaining  figures 
lire  the  halfpence  in  the  given  sum. 
1.     Change  1143  dols.  74  cts.  to  Irish. 
114374 
117 


8OO6I8 
114374 
114374 

2)133817158 

12)66908| 

2l0)557|3    8 

Ans.  £.278    15  8£ 

If  the  sum  is  dollars  only,  work  by  cither  of  the  following 
methods,  , 


152  EXCHANGE. 


2.    "Change  1537  dollars  to  Tfish. 

met] 

)37 
.3 


First  method.  Second  method. 

1537  at  45.   lOld,  1537 


45.    J  307      8 

Sd.   i  51      4 

2       J  12  \6 

h-     i  3  4     01. 


8d  ^      51     4     8  461      2         Massachusetts 

2      J      12   l6     2           J       115     5     6  Exchange  at  25  per  ct.. 
1  Q      /i      nl 

345    16     6  SterlincT 


Ans.£.374   12   10^        ^\       28   1()     4iEx.8ipr.Gt.orlJ.onl^. 
£.374   12   lOi 

In  changing  Sterling  to  Irish  money  at  par,  ^\  is  added  to 
the  sum  for  Irish  ;  and  in  chaHging  Irish  to  Sterling,  ~^^  is  de- 
ducted for  Sterling  because  12  pence  English  are  equal  to  13 
pence  Irish,  making  the  Exchange  Id,  in  a  shilling,  1^.  Sd.  in 
a  pound;  and  £,S  6  8  per  cent. 

Examples* 

1.  Change  £.394  17  5  Sterling  to  Irish,  at  par,  or  £.8| 
per  cent. 

,\)394^  17     6 
32   18      U 


Ans.  £.427   15     71  Irish* 

2.     Change  £.427  15  7|  Irish  money  to  Sterling,  at  83  per 
cent,  in  favor  of  England. 

^3)427 15  n 

32    18      U 


Ans.  £,394   17     6  Sterling. 

3.  Change  £.370  Sterling  to  Irish,  at  9  per  cent; 

£.  £.  £.  . 

100     :      109     :  :     370  Ans.  £.403     6     0 

4.  Ptcduce  £.403  6  Irish  money  to  Sterling,  at  9  per  cent. 

9 
100 

£.     s. 

109.       :       100     :  :     403    6  Ans.  £.370 


EXCHANGE.  ir>3 

HAMBURG  H. 

Accounts  are  kept  in  Hamburgh  in  Marks,    Shillings   Lubs 

or  Stivers,  and  Deniers. 

12  deniers,  or  2  grotes,  make*  •  •  •  1  shilling  lubs,  or  stiver. 

1()  shillings   lubs,  stivers,  or   7       ^  , 

oo         .  r      1  mark. 

32    grotes    ••••••#•••••••  j 

ALSO,       * 

12  grotes  or  pence  Flemish  make  1  shilling  Flemish 
20  shillings  Flemish •  •  •       1  pound. 

Note.  3  marks  •...••..  make 1  rix  dollar. 

7  5  do.  •  • 1  pound  Flemish. 

A  shippound  in  Hamburgh  •  •  •  •    280  lb. 

A  ring  of  staves  •  •  do. 240 

100 lb.  in  Hamburgh 107^  lb.  in  U.  States* 

100  ells.  .  •  do.  •• 62i  yards. 

The  currency  of  Hamburgh  is  inferior  to  the  bank  money  ; 
the  agio,  or  rate,  is  variable  ;  May  14th,  179S,  it  was  20  per 
cent,  in  favor  of  the  bank. 

The  mark  banco  is  33^  cents  ;   (See  Laxvs  of  the  U.  States.) 

Examples. 

1.  Change  12843  marks  to  Federal,  at  33}  cts.  per  mark, 

33j=:J)12843 

Ans,       4281  dollars. 

2.  In  4967  marks  8  stivers  banco,  how  many  dollars,  ex* 
t-hange  as  above  ? 

331-^)4967, 


8  stivers  ,l6^- 


Dols.      16'55,83 

Ans.  1655  dols.  83  cts. 


To  change  Ilamhirgh  7noncy  to  Sterling, 

Rule.     As  the  given  rate  is  to  one  pound,  so  is  the  Ham- 
haxgii  sum  to  the  Sterling  required. 


154  EXCHANGE. 

Examples. 

1.     Change  2443  marks  9|  stivers  to  Sterling,  exchange  at 
32^.  6d,  Flemish  per  pound  Sterling. 

*.     d,  £.  m,        St. 

32  6       :       1       :  :       2443       9i 
12  grotes.  32       2 

350  48 S6     19  grotes 

7329 
19 

78195 
1 

390)78 195  (200;^, 
780 

195 
20 


Ans.  £,200  10  0 


390)3900(10^* 
3900 


2.  In  12093  marks  12  stivers,  how  many  pbunds  sterling, 
exchange  at  32^.  3d,  Flemish  per  pound  SterJmg  ? 

Ans.  £.1000 

3.  In  4178  marks   2  stivers,   how  many  pounds  Sterling, 
exchange  at  31^.  lOd,  Flemish  per  pound  Sterling  ? 

Ans.  £.350 

4.  Change   1971  marks  13  stivers  to  Sterling,  exchange  at 
35^.  6d,  Flemish  per  pound  Sterling.  Ans.  £.148  2  4 


To  change  Sterling  to  Hamburgh  nw?iei/. 

Rule.     As  1  pound  Sterling  is  to  the  given  rate,  so  is  thft 
Sterling  sum  to  the  Hamburgh  required. 


EXCHANGE.  155 

Example. 

Change  £.350  Sterling  to  Hamburgh  money,  exchange  at 
3U\  lOd,  Flemish  per  pound  Sterling. 


£,        s,     d,  £, 

1     :     31   10     :   :     350 
12 


382  grotes 


350 


1()100 
1146 


2)133700  grotes 
1 6) 66850  stivers 

4178  2  Ans.  4178  marks  2  stii^ers. 

Proving  the  answers  in  the  preceding  case  will  further  exemplif]y  this. 


To  reduce  Current  to  Bank  money. 

Rule,     As  100  marks  with  the  agio  added,  is  to  100  bank, 
fco  is  the  current  money  to  the  bank  required. 

Examples. 

1.  Change  560  mfeks  8  stivers  current  to  banco,  agio  at  18 
per  cent. 

18 
100      . 

118  :   100  ::  560  8.   Ans.  475marks* 

2.  Change  2366  marks  current  to  banco,  agio   at  20  per 
cent.  Ans.   1^71  marke,  10|  stivers. 

3.  Change  7^56  current  marks  to  banco,  agio  at  22  per 
cent,  Ans.  6lll  marks,  7  stivers* 


156'  EXCHANGE. 

To  change  Bank  to  current  money. 

Rule.     As  100  marks  is  to  100  with  the  agio  added,  so  is 
the  bank  given  to  the  current  required. 

Examples. 

3.     Change  4/5  marks  banco  to  current,  agio  at  18  per  ct. 
18 
100 

m.  m. 

100    :    118  ::  475  Ans.  560  marks,  8  stivers. 

Or  thus, 

475 
18 


.3800 
475 

560  8  as  above. 

851 50 
16 

8|00 

2.     Change  1971  marks,  lOf  stivers  banco  to  current,  agi® 
^t  20  per  cent. 

m.  s. 

20   J) 1971  lOf  banco 

39^  5I  agio 

Ans.  2366  0     current. 


PRACTICAL  QUESTIONS. 

1.     How  much  will  634521b.  of  cotton  ccnie  to,  at  8  grotes 
per  lb.  ? 

lb.  gr.  lb. 

1:8::      63452 
8 


2) 507616  grotes 
16)253808  stivers 
Ans,         15803  marks* 


exchange:. 


157 


H.   What  will  35  lib.  of  cotton  come  to  at  5Qd.  per  lb.  ? 

Note.     d.  is  the  mark  for  pence  Flemisli,  ec^ual  in  valae  to  half  stivers  O'r 
^alt'shiJliu^s  lubs. 


lb. 

d. 

Ih. 

1     : 

:      50     : 

:     351 
50 

2)17550  grotcs  or  pence  flemisli. 


l6')S775  stivers. 


5^\^8  7 


Alls.  54S  marks  7  stivers. 


3,  What  will  33.9  bars  Ptussian  iron  come  to,  \vt.  1S062  lb, 
*t  35  J  marks  per  shippound  ? 

lb.  n.  Ih. 

280    :    35|     ::      I9662  Ans.  Q^O'^  m,  U  6tiv. 


4.  2801b.  of  cotton 

5.  4002i-  lb.  coffee « 

S.  2438  pipe  staves • 

7.  3510  hlid.  ditto - 

8.  529  barrel  ditto -^  •  •  « 

9.  1790  lb.  stignr 

10.  4892  lb.  rice 

11.  4  pieces  10-4  bcdiick  .  •  •  • 

1 2.  140  half  pint  tumblers 

13.  1)0  boxes  windo-.v  rlass  •  •  •  • 

14.  lDi6\  lb.  coll'ee 

15.  245  hi  ;  iron,  vrt.  G4:i4  lb.  •  • 

16.  10  '     -s  he.T.p,  ■•  t.  14108  lb. 


at     21  grotes  perlb.     •  183  12 

8|  stivers -..-....  2063  10 

16  marks  per  ring  of  240    •  •    162     9 

8|  ditto         ditto 1^5    -6 

5^  ditto         ditto 11     9 

•      21^  pence  per  lb. 1188   it) 

lo^  marks  per  100     • 892   12 

24     ditto 96     0 

0     ditto  per  100 11     3 

23     ditto  ])er  box 2^00 

•        16^-  stivers  per  lb. 1574     3 

41  marks  per  shippound  •••  •  li?35 

74  ditto         ditto 3723 


17.  V  iiat  is  I.  J  commission  on  18270 marks, at  2r>  per  cent.? 

Ans.  45^  m.  12  st. 

18.  What  is  the  interest  of  6370  marks,  for  3   months,  at  5 

.     ^  ^j^g    jf^  j^^^    ^^  ^^ 


per  cent,  per  annum  ? 


O 


ioS  EXCHANGE. 

19.  Change  5955  marks  71  stivers  to  Dutch  fioriiis,at  38| 
grotes  per  liorin. 

mar.         st. 

5955    7k 
grotes  in  a  markzz  32     2  orrotes  a  stiver. 


]  1910  15  grotes  in  7h  stivers 
17S65 
15 


grotes  38|     190575  grotes. 
2  2 


77  )   381150  (  4950  gilders. 
308 

Til 

693 

.,^  385 
385 
Ans.  4950  gild,  or  flot. 

20,     An  American   merchant  orders  his  correspondent  in 
Amsterdam  to  remit   49S0  florins  l6g  stivers  to   Hanrtburgh  5 
this  being  done,  when  the  exchange  is  39i  stivers  for  2  marks, 
what  sum  is  he  credited  for  in  Hamburgh? 
St.  M.  F.        St. 

S9l     :     2     ::     4980  1(3| 
4  20        '^ 

157  996l6i 

2 


199-233 

4 


157)796"932(507^  marks 

785 


1193 
1099 


942 
942 
'  "     Ans.  5076  marks* 


EXCHANGE.  159 

HOLLAND. 

Accounts  arc  kept  in  Florins  ov  Gilders,  Stivers,  Deniers  or 
Pcnnings. 

8  pcnnings make  •  •  • 1  grotc. 

2  grotes,  or   1()  pennings    •  •  •  • 1  stiver. 

20  stivers,  or  40  grotes  " •    1  gilder  or  florin. 

ALSO, 

12  grotes,  or  6  stivers l  shilling. 

20  shillings,  or  6'  gilders  • .  - .  • 1  pound  Flemish. 

2h  florins    •  •    1  rix  dollar. 

The  florin  or  gilder  of  the  United   Netherlands  is  estimated 
in  the  United  States  at  40  cents,  or  2  cents  per  stiver. 

100  lb.  in  Amsterdam  make  109|  lb.  in  the  U.  States. 

100  ells»  •  •  •do.*  •  •  • 75  yards  do. 

Ill  liquid  measufe,X6' mingles  make  1  stcckan,8  stcckaus  1  aum. 


1.  Change  1954;  florins  to  Federal  money, at  40cts.perflorin. 

1954 
40 

dols.  781,00  Ans.  781  dels.  60  ct% 

i 

2.  Change  2653  gilders  17  stivers  tO   Federal  money,  at  40- 
cents  per  gilder. 

2653      17  Or  thus,     2(V.''i.3      17 

40       2  20 

1061  .^0     34         .  5^077  stivers. 

34  2  els.  per  stiver. 

1O01j4  cts.  1001,34 

■    Ans.  1061  dols.  54  cts. 

3.  Change  lO^I  dols.  54  cts.  to  gilders,  at 40  cts.  per  gilder. 

2)  1 06' 154  cents. 

2|0)53O7l7  stivers. 

^53  17         Ans.  2()53oild.  I7  5tiv. 


I 


169. 


EXCHANGE. 


3.  What  must  be  paid  in  Boston  for  an  invoice  sfgoods  charg- 
ed at  ,5.91  florins  17  stivers  ;  allowing  the  exchange  at  40  cents 
per  florin,  or  2  cts.  per  stiver,  and  advancing  on  it  60  per  cent.? 
591    17 


20 


<^. 


11837  stivers.  Am,  of  invoice,  23G  74 

2  Advance,   142  04 


•lols.  23(),74  Ans.  378  7S 

60  per  cent. 

142,0440 


To  change  Sterling  to  Flemish, 

KuLE.     As  1  })oimd  sterling  is  to  the   given  rate,  so  is    t|i« 
sterling  given  to  the  Flemish  required. 

Examples. 

1.     In  i^.lOO  \Qs.  sterling,  how  many  gilders,  exchange  at 
035.  9d,  Flemish  per  pound  sterling  ? 
£.         6.  d.  £.     s. 

1      :     33  9     ::     300  IQ 
20  12  20 


20        405  grts.       2010 
405 

10050 
80100 


210)81405,0 

2)40702.^  grotes. 


2lO)2035|l|  stivers. 

1017   11|  Ans.  10 17  gild.  Hi  st. 


% 


To  change  Flemish  to  Sterling. 

Rule.     As  the  given  rate  is  to  £.1  sterling,  so  is  the  Flem* 
isk  given  to  the  sterling  required. 


IIXCIIAKGE.  I'ST 

Example. 

Change  1017   gilders   llj   stivers  to  sterling,  exchange    at 
536-.  9^/^ Flemish  per  £,  sterling. 

s,  d,         £,  fl.         St. 

33  9     :      J      ::      1017     Hi 
12  40        2 


405  grotes.  40(580     22j 

22i 


4.03)407  02K 100' 
405 

202i 
20 

405)4050(10 
4050 
Ans.  £.100   10> 

^'  To  change  Current  Money  to  Bank. 

Rule.     As  100  gilders  with  the  agio  added,  is  to  100  bank^ 
«o  is  the  current  money  given  to  the  bank  required. 

Example.  ^^ 

Change  823  gilders  pj  stivers- current  mone}^.  into  bai^,  ag!«» 
at  4^  per  cent. 

g'  g'  g'     -y- 

104 J      :      100     ::      823  pi 
20"  2.0 


.2090  164691 

100 


2O9O)l046'C)2O(78S  gilders. 
To  change  Bank  Money  into  Current, 

Rule.     As  100  gilders  bank  is  to  100  with  the  agio  addedp. 
so  is  the  bank  money  given  to  the  current  required. 

Example. 

Change  7^^  gilders  bank  money  to  current*,  agio  at  4|  percent^- 
g,         g,  g, 

ZOO  :   1041  ::  7SS         Ans.  823  gilderS;  9j  stiv. 


l62  -    EXCHANGE. 

PRACTICAL  QUESTIONS. 
I.  Wliatwill  1867  lb.  ot  cofiee  come  to  at  IQ  stivers  pcrllo 

3  867 
19 

16803 
1867 


2|0)3.>47  \3  stivers. 

1773  13  Ans.  1773  gilders,  13  stivers. 

2.  What  will  9-  hhds.  of  sugar  come  to,  wcighino;  104'242  lb, 
gross,  deducting  2  per  cent,  tor  good  weight,  tare  iH  ^er  c^^l,. 
at  21  grotes  per  ib.  ? 

104^42  ' 

deduct  2  per  cent.       2085 


102157 
•are  18  per  cent,         183B8 


83769  nt.  wt. 

21 


8>769 
167538 


2)1759149  grptcs. 


^^     ■  $|0)87957|4i  stivers. 

43978     14|  Ans.  43978  gilders,  14 J  stivers. 

5.     What   will  251  brirs  of   iron   come  to,  weighing  gross 
10364'  ib.  ^t  9j  gilders  per  100  ib.  deducting  2  per  cent.  ? 
10364 
H 


931^76  g.        s.    p. 

^l^  2pr.ct.=:5^o)i^iO     y   U 

'^0      4      3 


2591 


1010,49 

9,80 
16 

12,80 


EXCHANGE.  l63> 

4.     What  will  143  stcckauh  2  mingles  of  brandy como  to  at- 
42  gildeiii  per  auai  ? 

8)14.3 

17     7     2- 

S4 

48tPClvans     J         21 
2 I  10  10 

1    i  5     5 

2  miugles     |  0   13     2 


751     8  2  Ans.  751  gild.  8stlv.  ^ppnnmgSr- 

5.  ?1315  lb  of  sugar 23  grotes  per  lb. 1^:2'56     2 

6.  56560    25 35.i50 

7.  v7()9J    25^ 17'>71    15 

8.  8 1 H9  ib.  coIFee ^o{  st.vers !:>622     1 

9.  4650 23^ 5405   1 2 

10.  U)7  ) 19J 1945     7 

11.  39285 2i;-   417^0     6 

12.  212  f  lis  liiien,  208  pasabk  30    312 

l.J.  4l«0lb   buuei- 13  aiki    pcr4()ib,..-.    1.61   1.5 

14.  6i76 lU 1861    17 

15.  2012  ib.  lend l.S^  do   per  100    lb...      271    12 

lb,         2l4&lcck.  11  ming.  biHiui^V  42    do.  per  aum    ••••    1127     2 


D  E  N  M  A  R  K.  •^ 

Accounts  art?  kept  in  Danish   current  dollars  and    skillingsy . 
rcckonmi;  yObKillinvJs  to  the  dollar. 

The  Course  ot  exchange  on  London  in  September,  1799,  was- 
5  rix  or  Danish  dollars  tor    1  pounct  stcrhno;.  % 

The rwc  dollar  ot  Dennuirk  is  ebluii.acd  at  100  cents. —  CSce 
Laws  of  the  UnitcH  Sfnfcs.) 

i;ti  pounds  ot  Denmark  make  ICO  pounds  in  the  U.  States, 

Ul.eir  weights  arc  shippounds,  lispounos  and  pounds — 

10  p(iunds    make    1    lispiaind. 

20  II- pounds,  or  3*20 pounds 1    shippuund. 

1.     How  much  will  8  pieces  of  platillas  come  to,  at  9  doh, 
5(xbkiLs,  per  piece? 

9     56 
8 

76    64  Aos.  76  doU  64  skills. 


164  EXCHANGE. 

2.  How  miicli  will  1418  bars  of  iron  come  to,  weighing  2^3 
shippoijnds  9  lispoundsand  4  pounds,  at  15  dols.  pcrshippound? 
lb.        d,  s.   lis.  lb.  Or,  ship, 

320  :    15    ::    26'3  9  4  263 


20  15 


5769  Us,       3945 

}6  5     ;^  3  72 

4     J  3  00 


31^18  4/6.1^6        0  18 

5269  

Ans.  3951  90 


84308 
15 


3210)12646210(3951 

304 
2.88 

"166 
160 

~2 
32 

30 

9^ 


32)2880(9© 
♦       2880 

. Ans.  3951  dols.  90  sk. 

3..  What  is  the  commission  on  21545  Danish  dols.  13  skiH^ 
At  2  per  cent.  ? 

21545   13 
2 


430,90  26 
810 


«6,66  Ans.  430  dols,  86  sk^lki 


EXCHANGE.  165 

4.  What  will  4  hhds.  of  sugar  come  to,  weighing  gross  4314> 
lb.  tare  17  per  cent,  at  22  skillings  per  lb.  ? 

.     Ans.  820  dols.  62  skills. 
dfs.  s\s.  dls.  shs- 

5.  4  pieces  table  cloth    S  80 15  32 

6.  50   9  56 479  16 

7.  13   17  64 229  64 

8.  24   12         288  00 

9.  50   15         •  750  00 

10.  100  coils  cord,  wt.  62sh.  i6L  'lib.  .30  pershippound  1884  18 

11.  85  bun.  cl.  hemp,  250  36     •• 9000  00 

rz.     1951  bars  Rus.  iron,  362     8  10         14     5074     3 

13.  How  many  Danish  dollars  will  be  received  in  Copenha>* 
gen,  for  a  bill  of  £.2300  on  London,  exchange  at  5  rix  dollar* 
por  pound  sterling  .?  Ans.  1 1500  dols. 

14.  A  bill  is  drawn  inCopenhagen  for  18574  marks,  7  stivers, 
Hamburgh  money,  v;hen  the  exchange  is  128  Danish  dollars  for 
3  00  rix  dollars  in  Hamburgh,  how  many  Danish  dollars  does  it 
amount  to  ? 

^^oTE,     Three  marks  are  equal  to  1  rix  dolla»» 

m,  r.d.         m,     st,     r.d,     sk. 
If  3  :   1   ::   18374  7  :  ^Ipl  46*  • 

r.d,     D.d,         r.d,     sic. 
If  100  :   128  ::  Cngi  46         Ans.  7925  Dan.  dols.  6sk. 
Or  thus,  3)18574    7  Hamburgh  money. 

6191   46 
28  per  cent.     1733  56 


79^5     6  Dan.  money,  as  above. 

B  R  E  M  E  N. 

Accounts  are  kept  in  rix  dollars  and  grotes,  reckoning  72 
grotes  to  the  rix  dollar,  which  is  equal  to2i  marks. 

On  the  29th  Nov.  1795,  the  exchange  on  London  was  551 
rix  dollars  lor  .£.100  sterling. 

In  1802,  the  course  of  exchange  on  the  United  States  was 
75  cents  per  rix  dollar. 

The  Bremen  last  is  equal  to  80  bushels  in  the  U.  States. 

100  lb.  in  Bremen  ^re  equal  to  110  lb.  in  the  U.  States, 


l66  EXCHANGE. 

1.  Wliatuiil  11041b.  of  coffee  come  to  at  32^  grotes  pcrlb.  ? 

1104. 
32| 

2208 
3312 

552 
276' 
■  r.d.  s;rote&f 

72)36156(502   12 
360 

156 
144 

12     Ans.  502  rix  doTs.    12  grofe** 

2.  What  is  the  commission  on  7621  rix  dols.  6  gr.  at  S^pesfr 
cent.  ?  ^  Ans.  266  rix  dols   53  grotes. 

r.  dots.  gr. 

3.  3071  lb.  coffee   ••   32i  grotes  per  lb.   ••    135/6  63 

4.  400    32|  ••- 181    18 

5.  706    .# 33^ 328  35. 

6.  31407  lb.  sugar   ...   15^  ••• •••••    6870  2P 


A  N  T  W  E  R  P. 

Accounts  arc  kept  in  Antwerp  in  gilders,  shillings,  and  grotes, 
12  iirotes  •  •  •  •  «• make 1   shilling. 

3^  shillings,  or  40  grotes     1   gilder. 

The  Braband  or  Antwerp  grotes  are  of  the  value  of  the  cents 
of  the  UnigEd  Stato'^,  a  gihier  being  reckoned  at  40  cents.      In 
the  current  money  ot  Antwerp  t!  ey  have  slivers  of  the  value  of 
the  stiver  of  Anisterdam,  or  2  cents  United   States  currency. 
100  pots  Braband  rz  36;^j  gallons  U.  States. 

<)6  ib.  Antwerp  ■=:  100  lb.  do. 

100  Bral)and  ells,  about  74  yds.  American. . 

The  new  quintal  of  Antwerp  consists  of  JO  myriagrammesor^ 
204  lb.  14  oz.  Avoirdupois  weight.  , 

The  loss  on  sugar  exported  from  America  to  Antwerp  is  22  J 
per  cent.  viz.  tare  14  lb.  per  100  ib.-^good  weight  2  lb.-  -loss  - 
of  weight  5  lb. — discount  Ij  lb.  equal  to  22^>  ib.  per  lOO  lb. 

Loss  gn  cotton  i2|  per  cciit.— -on  cofici^  ia  bags  1 1^  per  cent* , 


Exchange.  isr 

Examples. 

1.  A  cargo  consisting  of  48  hhds.  sugar,  weighing  37^  cwt. 
1  qr.  14  lb.  valued  per  invoice  at  12  dols.  per  cwt.  and  63  bags 
cofiee  weighing  7345  lb.  at  32  cents  per  lb.  is  sold  in  Antwerp; 
what  sum  wa-.  received  for  it,  in  gilders  and  grotes,  at  40  cents 
per  gilder,  allowing  the  customary  deductions  for  tare,  ike.  at 
an  advance  of  33 3  pe^  cent,  from  the  invoice  ? 

cwt.  qr.   lb.  Ih. 

376  1    14  .        7345 

Tare,&c.22^perct.  84  2  20|  Tare,&c.lljpcrct.  844|- 

Neat         291  2  22 J  Neat  6jOOJ 

• 32 

Ms.  cfs.  1300Q 

12  00  19500 

10  16 

120  00                             ^ols.  2080,16 
10  . 

1200  00 
^ 2 

2400  00  val.  of  200  cwt. 

1080  00 90 

12  00 1 

6  00 2  qrs. 

1    50 14  lb* 

75 7 

10  7 1 

5  3  ....  i 

Value  of  sugar        3500  41   0           291   2  22| 
do.       coft'ee        2080    16  0 . 

5580  57  0  4|0)74407!5  centsi^ 

Adr.  331  =  3        ^^(^0  19  0  

IS601  36 

Dols.       7440  76  0  

— ' —  Ans.  I8COI  gild.  36  gr. 


it)8  EXCHANGE. 

2.  What  sum  must  be  paid  in  Boston  for  an  invoice  oF  goo^s 
imported  from  Antwerp,  amounting  to73J3  gilders,  exchange 
40  cents  per  gilder,  at  an  advanse  of  40  per  cent  ? 


7315 
40 

per 

cent,  ( 

7315 
idv.                2926  adv. 

2926,00 

10241 

40  cents  per  gild 

f.-. 

4096,40 
Ans.  4096dols.  40ct 

R 

U  S  S  1  J. 

Accounts  are  kept  in  Petersburgh,  in  Rubles  and  CopccSj 
beckoning  100  Copccs  to  1  ruble. 

The  course  of  exchange  on  London,  in  July,  17^6,  was  S4.f  J, 
sterling  per  ruble. 

Ditto  ••••  on  Amsterdam  ••*•  30  stivers  banco  per  ruble. . 
Ditto  ....  on  Hamburgh,  Aug.  1798,  22j  st.  banco  do. 
Ditto  •...  on  U.  States,  Sept.  1802,      55  cents  do. 

100  lb.  Petersburgh  weight  are  equal  to  SS|  lb.  in  theU.  States, 

Their  weights  are  Barquits,  Poods,  Pounds,  and  Zollotnicks--r 

96  zoilotnicks  ........  make 1   pound. 

40  pounds   •.•.........•. 1    pood. 

10  poods      1    barquit. 

Their  long  measure  is  the  Arsheen,  of  2S  American  inches  : 
^  aroheens  are<?qucd  to  7  yards, 

1.  What  will  7500  arshccns  of  ravcns-duck  come  to,  at  14| 
rubles  for  50  arshoens  ? 

arsh.  rub.  arsh. 

^0     :     14i     :;     7600  A-ns.  2l75ruble8U 


EXCHANGE.  169 

5.  What  will  813  poods  5  lb.  of  dean  hemp  tome  to,  at  S0| 
rtilbkvs  per  barqi^t  ? 

Ih.         rub.  p.    lb,  ^ 

400    :    301     '  •     6^3  ^ 
40 


975750 
16262 


:     # 


ii\00)9920\V2 


2480,03 

.  Aiis.  2480  rubles  3  copies. 


3.  What  will  2846  poods  5  lb.  of  bar  iron  come  to>  at  200 
^siopecs  per  pood  ? 

2846 
200 


.569200 
5  lb.  I  <zo 


copecs  569225 

i-  Ans.  5692  rubles  25  copecs. 

4.  What  is  the  commission  on  5256  rub.  33  cop.  at  3  per  ct.? 
5256,33 


Ans.  157  rubles  68  copecs. 
rub.  cop. 
24  rubles  per  50  arsheens.     2398  80 
.'H  co()ecs.  per  arshccn.  .576 

100     do.  do  355 

110     do.  do.  130  62 

21  rubies  per   piece.  4200   ^ 

31     do    per  barf[uif.  6515  04 

11.  How  many  rubies  must  be  received  in  Petersburgh  for  a  bill  of  15500 
■Riders  oil  Amsierdarn,  when  the  exchange  is  30  stivers  per  ruble  ? 
St.  cop.  gild,  ^if'-'- 

Aii  30     :      100     ::     15500  Or  thus  |U  5500 

20  5166.66^ 


157,68,99 

5. 
6. 
7. 
8. 
9. 
10. 

4997|  arsheens  flems 

1700      do.       drillings 

355      do.    '  ticking 

118|:    do.            do. 

200  pieces  of  sail  cloth 

2101  poods  25  lb.  hemp 

3100«:T0  stivers.                          10333,33| 
100  


$10)3100000lO 


10333,3  J I 
P 


■0 


EXCHANGE. 


12.  A  bill  of  ^.3000  Sterling  is  drawn  on  London,  ex- 
change at  31|f/.  Sterling  per  Ruble,  what  is  its  value  in  Pe- 
te rsbur2;h  ? 


(L 

As  3  1  ^ 
4 

rub.              £, 

:      1      ::      3000 

-    20 

127 

60000 
12 

72CC00 
4 

- 

127)2880000(22677  rubles 
254 

340 

254 

860 
762 

980 
889 

910 
889 

127)2100(16  copecs 
127 

830 

762  Ans.  22677  rub.  l6  cop. 

"is" 

Two  cyphers  are  annexed  to  the  remainder  instead   of  mut- 
t inlying  by  100  copecs. 


FRANCE, 

12  denicrs  rr:  1  sol,  20  sols  ~  I  livre. 

The  crown  of  exchange  is  3livrcs  tournois. 

A  livre  tournois  of  France  is  estimated  at  ISh  cents  m  the 
United  States. 

Note.  Tiic  wor.l  toimiois  is  applied  to  the  money  of  Frtvace^as  slcilmg  is 
(q  iJje  money  ot"  Eji^laiid. 


EXCHANGE.  in 

1.     Change  .£.1220  sterling  to  French  money,  exchange  at 
IZyfi.  per  crown  of  3  livres  tourno/o. 
cL       lit.         £, 


7i   :   3   ::    12'20 

8                       20 

.  1                 i.'4400 

12 

292800 

8 

2342400 
3 

141)7027200(49838  livres 
564 

% 

1387 

1269 

1182 

1128 

540 

423 

■^^ 

1170 

JtHk 

1128 

H 

42 

^^ 

20 

141)840(5^. 

705 

135 

12 

141)1620(1  ft/. 

141 

210 

141 

69     Ans.  49833  liv.  ^  sol.  11  den. 


n2  EXCHANGE. 

2.  .  Change  ^.400  sterling  to   French  money,  exchange   j!A- 
V^id.  feterliiig  per  crown  of  3  Ifvrcs.  Ans.  ii}2Zb  Ijv.  7*'.  b|ft/,. 

3.  Chano;e  4<'2'24  livres    tournois  to    sterling,    exchange   at 
17 Aa.  per  crown  oi  3  livres. 


liv. 

d. 

Uv. 

3   : 

^\ 

:  :  4224- 
^71 

Q956S 

4224 

.   2112. 

51)73920 


12)24640 


2|0)205i3  4- 

102    13  4 
Ans.  ^.1G2   13s.  4d. 

Or,  Tiil^?  ?^  of  the  given  sum  to  reduce  it  to  crowns,  aud 
Biultiply  by  the  rate  of  exchange  ;  the  product  will  be  the  an-« 
fwcr  in  pence. 

J)4224  livres- 


1408  crowns 
17i 


9^56 
1408 
704 


i2)24()40  pence 
2|0)205|3  4 


£.102   13  4  as  above. 

4.  Change  4<}S3S  livres  5s..  il|fc/.  to  sterling:,  exchange  at 
17 ^d.  sterling  per  crown.  Ans.  X.  1220. 

5.  What  will  2434  velts  of  brandy  come  to,  at  320   livres, 
per  29  velts  ?  ^  Ans.  26'857  liv.  18s.  7d. 


EXCHANGE.  173 

61'    What  is  the  freight  of  3302 J  vclts,  at  9  livres  per  ton  of: 
120  veils  ?  ^      Ans.  247  liv.  135.  C)d. 

7.  What  is  the  commission  on  3^591  liv.  2s.  4  den.  at  2| 
percent.  ?  Ans.  9^^  li^*'  155.  6  den. 

8.  AVhat  is   the    interest  of  6647(5  Hv.    lOs,   9  den.  for  1. 
month  and  10  days,  at  h  per  cent,  per  month  ? 

1)66476  10     9 


332(38 

5 

\ 

20 

7  C)5  ■ 

12 

7|S4 

332 

7 

■7 

10  days  J   110 

15 

10 

Ans<  Liv,  443 

3 

5 

g.     What  is  the  interest  of  3255  livres,  for  28  days,  at  J  per 
sent,  per  month  ? 

.        1)3255 


l6|27 
20 

10 

5150 
12 

6l00 
16     5 

6  for  om  month 

13  days  J     8     2 

10  .....  A     5      8 

3  ....  J      112 

9 
6 

n 

i^ 

Ans.  Liv,   15     3 

1 

p' 

The  present  money  of  account   in  France  is  in  francs   and 
centimes  or  hundredths. 

In  Nov.  1800,  an  English  guinea  was  worth  25  fr.  7o  cent, 
A  Spanish  dollar  •••.»♦    5  do.  53   do, 
P2 


17^  EXCHANGE. 

To  change  francs  to  litres  tournois. 
Rule.      Multiply  the  irancs  by  8i  and  divide  by  80  for  \i- 
vrcs. 

Example. 

Change  3755  francs  to  livres. 
3756 
81 


3756^ 
30048 

8,0)30423,6 

3802   76 
20 


8,0)152,0 

\9  Am.  3802  If  v.  I9  sols. 

To  change  litres  tournois  to  francs. 

Rule.     Multiply  the  livres  by  80,  and  divide  the  product 
by  St  tor  francs. 

Example. 

Change  5469  livres  to  francs. 
5469 
SO 


81)437520(5401,43 
405 


325 
324 


120 
81 


390 
324 

260 
243 


17  Ans,  6401  fr.  4J  gce*. 


EXCHANGE.  17i 

To  change  sols  and  denier s  to  centimes. 

Rule.      Take  one  half  of  the  sols  and    dcniers,  as  if  they 
were  integers  ;  this  half  is  the  number  of  centimes  required. 

Examples. 

sd.  den,      sot  den.     sol.  den.  ,   sol.     dcii. 

Change  4     6       12     2       6     ^       l6     6  to  centimes. 


Ans.  23  6l  34;  83  centimes. 

When  there  is  a  remainder  in  dividing  the  sols,  it  is  to  be 
carried  to  the  deniers,  and  reckoned  10  and  not  12  ;  add  this 
10  to  the  deniers,  and  take  one  half  of  the  sum  for  the  remaia- 
ing  centime. 

Examples. 

sol.     den.  sol.  den.  sol.     den. 

Reduce    58  154  19     6'  to  centimes 


Ans.  29  77  98  centimes. 

If  the  number  of  deniers  be  10  or  11,  they  are  to  be  reject- 
ed, and  in  place  of  them  you  are  to  add  1  to  the  number  of 
sols  preceding,  aiKl  then  annex  a  cypher  to  it  ;  one  half  of  thi* 
is  the  centimes  required. 

Examples. 

sof.     den.  sol.     den.  so!,     den. 

Change     1      10  7      H     and    15      10    to  centimes, 


2)20  2)80  2)l60 


Ans.    10  40  80  centimes. 

Sols  and  deniers  are  reduced  to  centimes  by  the  preceding, 
rule,  and  though  the  result  is  not  accurate,  yet  from  its  sim- 
plicity and  conciseness  it  is  generally  used. 


nS^  EXCHANGE. 

TABLES 
For  eiiANGiNG  Livres,  Sols  and  Deniers  to  Fraxcs" 

AND  CENTIMES. 

[N.  Br     The  first  is  sufficiently  exact  for  business  ;   in  the  second   the  answer' 
is  calculated  to  the  ten-thousandths  part  of  a  centime.] 

Tab.  L                         Tab.  II. 

iJemers.  It,  Cent,                 Fr.  tent.          ^„„r 

1  ........  0  0  0 

2     0  1  0 

3     0  1  0 

^"            4     .. 0  2  0 

5     0  2  ...   0 

*                  6       0  2  ..  .  .   0 

7 0  3  0 

8r     0  S  0 

9 0  4  0 

10     0  4  0 

11     0  5  0 

Sols. 

1      0  5  0 

2      0  10  0 

3      0  15  0 

4      0  20  0 

.5      0  25  .....*..    0 

6      0  30  0 

7      0  35  0 

8     0  40  0 

9     0  44  0 

10     0  49  0 

11      0  54  0 

n     0  59  0 

13      0  64  0 

14     0  69  0 

15     0  74  .    0 

16       ...  0  79  .    0 

17     0  84  0 

18      0  89  0 

19     0  94  ....*•'.   0 

lAcres. 

1     0  99  0 

2     1  98  1 

3     2  96  2 

4     3  95  3 

5     4  94  4 

6     5  93  5 

7      6  91  6 

8     7  90  7 

9     8  89  .» 8 

10  ...,,,..  9  88  ^^ 


0 

4115 

0 

8230 

1 

2346 

1 

6461 

2 

0576 

2 

4691 

2 

8807 

o 

2922 

3 

7037 

4 

1152 

4 

5267 

4- 

9383 

9 

8765 

14 

8148 

19 

7531 

24 

6914 

29 

6296 

34 

5679 

39 

5062 

44 

4414 

49 

3827 

54 

3210 

59 

2593 

64 

1975 

69 

1358 

74 

0741 

79 

0123 

83 

9506 

88 

8889 

93 

8272 

98 

7654 

97 

5309 

96 

2963 

1)5 

0617 

9:> 

8'i^72 

92 

5<>26 

91 

3580 

90 

12^5 

88 

8nb9 

87 

CJ'VS 

EXCIIANGi:. 


177 


Livres. 


Fr.  Cent. 


12  11  85 

1.5  14  81 

20  19  75 

24  2o  70 

30  20  63 

40  39  ;)  I 

50  49  38 

60  59  ^6 

70  69  14 

72  71  11 

80  79  01 

90  ......  88  89 

96  94  81 

100  98  77 

200  197  5.1 

300  296  30 

400  395  06 

500  493  83 

1000  98?  65 

6000  • .  4938  27 

10000  9876  54 


Fr.  Cent. 

.  11  85 

.  14  81 

•  19  75 
.  23  70 
.  29  62 

•  39  50 
.  49  38 
.  59  25 
.  69  1$ 
.  71  11 
.  79  01 
.  83  88 
.  94  81 
.  98  76 
.  197  53 
.  296  Q9 

.  3':\^  06 

.  493  82 

.  987  65 

4938  27 

. 9876  54 


iOyOOOths  of 
a  centime, 
1852 
4815 
.3086 
3704 
96:30 
6173 
2716 
9259 
5803 
1111 
2346 
8889 

4815  ^ 

5432  ^i 

08f)4  ^  ^ 

6^297 
1729 
7161 
4322 
1608 
3217 


For  reducing  FraN' 
Cent.  sol.  den, 


1  ' 

2  • 

3  . 

4  . 

5  . 

10  . 

15  • 

20  . 

25  . 

SO  . 
35 

40  . 

45  - 

50  • 

5.^  . 

60  . 

65  • 

70  . 

75  . 

IK)  . 

8.>  - 

90  . 

95  . 

Francs. 

1  . 


0  2 

0  4 

0  7 

0  9 

1  0 

2  0 

3  0 

4  0 

5  0 

6  0 
7 
8 
9 

10 
11 
12 
13 

14  2 

15  2 

16  2 

17  2 

18  2 

19  2 


A 

CS   AND  CeN 

tooths 
of  den. 

43 

86 

2 


TABLE 

TIMES  TO  Livres,  Sols  an©  Denie^i^ 


15 

30 
45 
60 
75 
90 
05 
20 
35 
50 
65 
80 
95 
10 
25 
40 
55 
70 
85 


liv.  sol:,  den, 
10       3 


Francs. 


liv.  sol.  den. 


4 4 

5 5 

6 6 

7    7 

8 8 

9 9 

10 10 

15 15 

20 20 

30 SO 

40 40 

50 50 

60    60 

70 70 

80 81 

90 91 

100 101 

200 202 

300 303 

400 405 

500 506 

1000 10  J  2 

5i)00 5062 

10000    10125 


0 
0 

1 
1 
1 
1 

2 
2 
2 
3 
5 
7 
10 
12 


15  O 

17  6 

0  0 

2  6 

5  0 

10  0 

15  0 

0  0 

5  0 

W  0 

10  0 

0  a 


178  EXCHANGE. 

SPAIN, 

Spanish  reckonings  are  of  two  sorts — 

Money  of  plate,  distinguished  hard  or  plate  dollars,  &c. 
INIoney  of  vellon,  distinguished  by  current  dollars. 
The  former  is  88  ^^  per  cent,  above  the  latter. 
100  reals  plate  being  equal  to  188^-7  reals  vellon. 

100  reals  vellon 53  J  do.  phite. 

17  reals  plate  •  •  • 32     do.  vellon. 

17  piasters  or  current  dollars  256  do.  do. 

4  maravadiesmake  1  quarto,  8|  quartos  or  34  inaravadies  1  real. 

The  peso,  piaster,  or  current  dollar  of  8  reals  plate,  passes 
€^yl5  reals  vellon  in  trade,  but  in  exchange  it  is  estimated  at 
xS  reals  vellon  2  maravadies. 

The  ducat  of  exchange  is  375  maravadies. 

The  real  plate,  is  estimated  10  cents,  and  the  real  vellon  at 

5  cents,  in  the  United  States. 
The  Spanish  arobe,  is  25  lb. 

100  lb.  of  Spain  is  97  lb.  English. 


To  change  reals  vellon  to  reals  plate. 

Rule.   I^Iultiply  the  given  sum  by  17>  and  divide  by  32  f©5 
reals  plate. 

Example. 

Change  800  reals  vellon  to  reals  plate, 
800 
17 


32)13600(4-25 
128 

80 
6'4 

160 

160  Ans.  425  reals  plate. 

To  change  reals  plate  to  reals  lellon. 

Rule.     ]\luliij)ly  the   given  sum  by  32,   and  divide   by  17 
for  reals  vellon. 


EXCHANGE.  17D 

Example. 


In  4,25  reals  plate,  how  many  reals  vellon  ? 
455 
32 


850 
1275 


17)13600(800 
130' 

00  Ans.  800  reals  vellon. 

To  change  reah  jJate  and  reals  t'cllon,  to  Federal  money, 

TlULE.      Multiply  ihe  retds  plate  by  10,  and  the  reals  vellon 
)>y  5,  tor  the  ccntb  ni  the  given  sum. 

Examples. 
1.     Change  14958  reals  plate,  to  Federal  money. 
14t)58 
10 


145^5, .^0  Ans.  145)5  dels.  SO  cts. 

2.     Change  \15^Z  reals  vellon,  to  Federal  money. 
17593 
5 

879,6'5  Ans.  ^7^  dols.  65  cts. 


CADIZ, 

Accounts  are  kept   by  some  ia  hard  or   plate  dollars,    reals 
Tcllon,  and  quartos. 

8  J  quartos make 1   real  vel'on. 

20    reals  vcUun  •  • I  (.iiiinr  ot  plate. 

Others   kooj'  ilieir   accounts  in  reals  phne   and  maravadics, 
reckoning  34  maravadies  to  1  real  plate. 

To  bring  reals  plate  to  dollars. 

Rule.      Multiply  the  ^iven    sum  b}    39,  and  divide    by  l7 
^or  reals  vellon,  and  uividt^  the  leais  vellon  hy  '<?0  for  dcliars* 


ISO  EXCHAIS^GE. 

Example. 

In  320  reals  plate  how  many  ha>rd  dollars  ? 
320 
32 


640 
96'0 

17)10240.(602  reals  velloB 
102 

40 
34 


6 

8J  2]0)60|2  reals  velloB 


17)31(3  quartos,  dol.  36  2  3 
51 

Ans,  30  dol.  2  r.  v.  3  q. 

To  change  hard  dollars  to  reals  plate,  , 

UtTLE.  Multiply  the  dollars  by  20  for  reals  vellon,  and  the 
reals  vellon  being  multiplied  by  17  and  divided  by  32  give  the 
real^  plate  required. — Or,  multiply  the  dollars  by  lOf  lor  reals 
plate. 

Example. 

In  l6  hard  dollars  how  many  renls  plate  ? 
16*  Or  thus,        \6 

20  lOf  16 

. 5 


320  l6t)  — 

17  10  8)80 


,2  240  170  il.  P»       10 

320 


32)o4-l0(170 
32 

224 

224  Aus.  IfO  reals  platt»i 


EXCHANGE.  181 

Practical  Questions, 

The  answers  to  xchich  arc  in  doUarSy  reals  tellon,  and  qvartos, 

1.     "What  "Nvill  4594^0  pipe  staves  come  to  at  80  piastres  or 
current  dollars  per  M.  or  1200? 

45940 
80 


12100)36752100 


3062f  current  dollars. 
S    reals. 


24501 J  reals  plate. 
32 


49002 
73503 


10| 


17)7840421 (461 2e 
68 

104 
102 

20 

17  2,0)46X2,0 


34  ^ols.  2o06  0   1 

34 

I7)22i(l 
17 

5|  Ans.  2306  h.dols.  0  r.  1  n. 

fi(i6t.  D.  R.  Q. 

^.       21800  barrel  staves  at  30|     per    1200  ••••   417  3  7 

3.  1200  hhd.        do.  40"        do.  ....      30   2  3 

4.  2  casks  sherry  wine         30        per  cask    • « t  •     45  3  4? 

Q 


18C  EXCHANGE. 

The  result  of  the  following  is  in  reals  plate,  and  maravadies^ 
5,     In  610 hard  dollars,  how  niany  reals  plate?  ; 

20  reals  vellon  zz.  1  hard  dollar. 


12200 
17 

85400 
12200 

32)207400(6481 
192 

154 
'    128 

2oO 
256 

40 
32 

8  Ans.  6481  r.p,  8  nlaf* 

6,     What  will  2632  barrels  of  flour  come  to^  at  1 1  current 
dollars  per  barrel  ? 
2632 
It 

28^52  piastres  or  current  dollars. 

8  reals  plate  ir:  1  piastre  or  current  doh 


Ans.    231616  reals  plate. 

7.     88  lasts  of  white  dry  salt,  at  6  piastres  per  last, 
88 
6 

528 
8 


4224  Ans.  4224  reals  plate^ 


EXCHANGE.  183 

8.     Change  £,600  sterling  to  reals  plate,  exciiange  at  36'|(/. 
sterling  per  piastre. 

600 
20 


12000 
12 


261       M40G0 
4  4 


145  )   576000  (  397'^  current  dnllars, 
435  8 


1410 
3  305 

31770 
3 

10 

1050 

1015 

31779 

10 

350 
200 

GO 
8 

145)480(5 
435 

1  reah» 

45 
34 

ISO. 
135 

145)1530( 
145 

10  maravadios. 

80  Ans.  31779  r.  p.  10  mar. 

9-     In  ^.3200  sterling^  how  many  reals  plate,  exchange  at 
3()]r/.  steriingvpcf  piastre*?  Ans.  1(;9489  r.  p.  22  mar. 


N.  B.     In  S\.  LucAR  accounts  arc  kept  in  Reals  plate   and  Qiraitos,  16 
(^uaitoi  lo  1  Ileal  plate. 


lU 


EXCHANGE. 
B  I  L  B  0  A. 


Accounts  are  kept  in  Reals  vellon  and  Maravadies,  34  mara- 
>adies  making  1  real. 

The  pound  in  Bilboa  consists  of  17  oz.  except  in  iron  whick 
is  but  l6*  oz. 

32  vclts  are  equal  to  66  gallons  in  the  U.  States. 

1 00  fanagues  • \5'2  bushels  do. 

100  varas*  ••••••  •    108 yards  do. 

To  change  piastres  or  cvrrcnt  dollars  to  reals  plate. 

KuLE.  As  1  current  dollar  is  to  15  reals  2  maravadics,  so 
is  the  given  sum  to  the  reals  required  ',  or,  multiply  the  sum  by 
1 5  reals  2  maravadies,  for  reals. 

Example. 
In  5000  current  dollars,  how  many  reals  vellon  ? 
2=  ,^7 )«000  Or  Uius,  5000 

15  2z=l   c,  dol,  2 


525000 
5000 
2^4     4 

75294^     4. 


54)10000 


Ans.  75294  r.  vel.  4  mar. 


To  change  current  dollars  to  sterling, 
RulTe.     As  1  dollar  is  to  the  rate  of  exchange,  so  is  the  gir- 
•n  sum  to  the  sterling  required. 

Example. 
In  5000  piastres  or  current  dollars,  how  many  pounds  ste'i^ 
ling,  exchange  at  3d^d,  per  dollar  ? 
p.  d.  p. 

As  1     :     361 


:     5000 
o6i 

180000 

1875 


12)181875 
210)151516  3 
Aus.  £,767  16  3 


5000 


S)  15000 
1875 


EX  CI  I A  KG  E.  IS^ 

To  change  sterling  to  current  dollars, 
Rule.     As  the  rate  of  exchange  is  to  1  dollar,    so   is  the 
given  sum  to  the  dollars  required. 

Example. 
In  £J7^7   \6s,  3(1.  sterling,  how  many  current  dollars,  ex- 
change at  36^(1.  sterling  per  dollar  ? 
(L         doL         £.  s,  d. 

As  o6|-     :       1      ::     7.37  16    3  Aiis.  5000  cur.  dols.  or  piast. 


To  change  sterling  to  reals  rello??. 
Rule.  As  the  rate  of  exchange  is  to  15  reals  2  maravadics^ 
so  is  the  given  sum  to  the  reals  required. 
Example. 
In  £A36^  10s.  sterling,  how  many  reals  vellon,  exchange  at 
36jj  sterling  per  current  dollar  ? 


r/. 

As  o6|    ; 
8 

r.  7n,         £.    s.  • 
lo  2    :  :     436    10 
20 

291     '  • 

8730 
12 

104760 
8 

2  mar 

.Z=j\      838080 

lo  2 

4190-1-00                       i 
838080 
49298 

29 t) 12620498(43369 
V1164 

980 
873 

lf)7i 
^73 

2010 
1746 

27;8 
2619 

119 

34  mar.~l  riuJ. 

Or,  838080 


34)167  6160  mar.  ^- 


49298  reals* 


291)4046(13  A;i%  ^i3:C9  rculs  13  man 

Q  2 


186 


EXCHANGE- 


Practical  Questions. 
1.     What  will  122  quintals  of  iish  come  to,  at  13^  reals  per 
quintal  ? 

122 
136' 


Ans.   16592  reals. 
2.     What  is  the  cranage  of  1137  quintals  offish,  at  10  ma*- 
ravadies  per  quintal  ?  ^  ^  - 


Ans.  334  R,  U  M. 


BARCELONA. 

The  monies  of  account  in  Barcelona  and   throughout  the 
Province  of  Catalonia  are  Livres,  Sols  and  Deniers. 

1 2  deniers make 1  sol. 

20  sols    > .1  livre. 

27 s  sols,  or  l|  livre 1  hard  dollar. 

28  sols  . .  • 1  cur.  dol.  the  piast.  of  exchange,^ 

To  change  litres  to  hard  dollars. 

Rule.     Divide  the  livres  bv  3  and  then  by  5  and   add  thf 
two  quotients  together  for  hard  dollars. 

Examples. 

1,  How  many  hard  dollars  in  360  livres  ? 
3    360 

120 
72 

192  Ans.  192  hard  dols. 

2.  How  many  hard  dollars  must  be  paid  for  an  invoice  (;if 
|pods  amounting  to  7134-  livres  ? 

3    7334. 

2378 
1426$ 


S804f  Ans.  SS04  h.  d.  SO  soU. 


EXCHANGE.  IS7 

To  change  hard  dollars  to  livres. 

Rule.   Add  to  the  given  sum,  the  half,  quarter,  and  eighth. 
Bf  it,  and  the  sum  will  be  the  livres  required. 

Examples. 

1.     In  192  hard  dollars,  how  many  livres  ? 


192- 
9G 
4S 

24 

360  Ans.  360  livreg. 

2.     IIovT  many  livres  in  3804f  hard  dollars  ? 


3804,8 
1902,4 

951,2 

^75,6 

7134,0  Ans.  7134  livres. 


To  change  livres  to  current  dollars. 

Rule.     Multiply   the  livres  by  5  and  divide   that  product" 
by  7  for  current  dollars. 

Example.. 
Change  271^  livres  to  current  dollars. 

2716 
5 


7)13580 


1940  Ans.  1940  cur.  dok. 


To  change  current  dollars  to  livres. 

Rule.    Multiply  the  current  dollars   by  7  and  divide   the 
product  by  5  for  livres. 

Example. 
Change  ]940  current  dollars  to  livres. 

1940 

7 

5)13580 

271^  Ar9,  27iaiivrMi 


188  EXCHANGE. 

P  0  R  T  U  G  J  L, 

Accounts  are  kept  in  Millrcasand  Rcas,  reckoning  1000  reas 
to  1  millrea  oi  5s.  72<^.  sterling,  or  1  dol.  25  cts,  in  the  U. States. 
A  vinten  is  20  reas,  and  5  \  inlens  is  a  festoon  of  100  reas. 


1.  Change  579  millreas  740  reas  to  Federal,  at  1  dol.  25  cts,. 
per  millrea.  M,  R. 

579,740  Or  tlms,  579,740 

1,25  I  added     144,935 

2898  700  Dollars    724,6/5 

69568  80 


Cents  72467,500  Ans.  724  dols.  67 J  cts. 

2.  Change  724  dols.  6712  cts.  to  millreas,  at    1   dol.  25  cts^ 
per  millrea. 

1,25)724,675(579  mill.  740  reas. 
Or,  deducting  J  from  the  sum   in   Federal  money  gives  the^^ 
millreas,  &c. 

Example.         |)  724,67  5 
144,935 


5 79?7 40  as  before. 

3.  Change  579  millreas  750  rcas  to  sterling,  at  5s.  7ld.  per 
miire  a. 

579J50 
67h 


4058,250 
34785,00 
289,875 

12)39133,125 

2iO)326|l       1 

Ans.     ^M63   1        Ij 

4.  In  ^.163   1   Ij  sterling,  how  many  millreas,  at  5<.v.  7h(h 
jlcr  millrea  ? 

s.       iL  7'cas.  £.     s.     (I. 

5      7!     :        1000     :  :        I63     1      ih 

Am,  579  mill.  750  reas"^ 


EXCHANGE.  189 

5.  What  is  the  commission  on  6245  mill.  46  reas,  at  2^  per 
teat,  ? 

6245,046 
I  2|  per  1,00 

12490092 
3122523 


156,12615         Ans.   156  mill.    126  rcag. 

6.  Suppose  a  cargo  is  sold  for  6245  mill  reas,  at  2  monthi 
credit,  for  prompt  payment  of  which  J  per  cent,  per  month  is 
allowed  ;  how  much  is  the  discount  ? 

^)6245  Or  thus, 

I  per  cent,  for  2  monthsnl  per  cen(. 

31,225  for  1  month.  6245 

2  1 


Ans.  62,450  for  2  months.  62,45 

7.  Suppose  you  import  596O  hhd.  staves  and  5060  barrel 
staves  on  which  there  is  a  duty  of  23  per  cent,  which  is  taken 
ki  kind,  how  many  of  each  remain  for  sale  ? 

Ans.  4590  hhd.  and  3897  bbl. 

M,  R.  M.    R. 

8.  702  barrels  of  flour  at  8,600  per  bbl.  • .  •  •  6037,20© 

9.  4590  hhd.  staves ,030  per  stave. ...  137,700 

10.     3897  bbl.     do.    ,020  per  do. 77,940 

XI..         71  alquiers  of  beans.  •    ,480  per  alquiqr  •  •  34,080 


Measures  of  Portugal. 

Cloth  Measvre, 

A  vara  is  43 §  inches  English. 
A  covedo  is  26f  ditto. 

Wine  Measure. 

1  almude  is  12  canados. 

1  canado  is  4  quarteels. 

An  almude  is  4^  gallons  English  wine  measure. 

A  canado  is  3  pints  Enjlisl^ 


^90  EXCHANGE. 

Corn  Measure, 

1  moy  is  15  fangas. 

1  faiiga  is  lour  alquiers. 

1  moy  of  Go  alquuTS  is  3  English  quartevs,  or  24  bushels  AVin- 
chester  measure. 

1  quarter  is  20  alquiers. 

1  English  bushel  is  2^  alquiers  in  Lisbon,  2  alquiers  in  Oporto, 
and  2  J  alquiers  in  Figuiras. 

A  moy  of  salt  is  the  same  measure  as  corn. 

A  pipe  of  coals  is  l6'  fangas. 

1   fanga  is  S  alquiers. 

A  pipe  of  coals  is  128  alquiers,  which  at  2j-  alquiers  per  bush- 
el, is  5l|  bu-jheis  English. 

Weights  of  Portugal. 

1  quintal  is  4-  arches. 

1  arobe  is  32  pounds,  so  that  a  quintal  is  128  lb.  Portugal  wt. 
which  is  equal  to  about  132  lb.  English,  avoirdupois  wci.lit. 
A  pound  is  about  l6J  ounces  English, 

Loss  ^j/  exchanging  English  money  inPortuguL 

An  English  guinea  passes  at  Lisbon  for  3  m.  ()00   r.  which  is 

134  reas,  or  9  pence  less  than  the  value. 
An  English  crown  passes  for  800  reas,  which  is  89  reas,  or  G 

pence  less  than  the  value. 
An  English  shilling  passes  for  \G0  reas,  which  is  18  reas,  or  a- 

bout  1.^  penny  less  than-  the  value. 


L  E  G  II  0  R  X. 

Accounts  arc  kept  in  Piastres,  Soldi,  and  Dennri,  reckoning 
12  deniers  to  1  soldi,  and  20  soldi  Jtp  1  piastre  or  dollar  of  48'A 
sterling  at  par. 

1  J  paul,  or  2  sols,  are  equal  to  I  livre. 

6"    livres 1  piastre  or  dollar. 

5|-  livres  (effective  money)   •  •     1      do. 
1    ducat 1  J  do. 


EXCHANGE.  ISl 

Weis^lits — A  pound  is  only  12  ounces  in  all  commodities. 
145  lb.  is  said  to  be  cqi.uil  to  the  English  quintal  of  112  lb. 
but  fish  generally  renders  about  156'  to  138  lb.  per  quintal. 

145  lb.  in  Leghorn     make     112  lb.  in  the  U.  States. 

4  brasses 1  cane. 

100  brasses 6'4  yards,  U.  States. 

1  palm •  •  • 9j  inched",     do. 

4  sacks  are  2  per  cent,  less  than  an  Lnglish  quarter,  of  8  bushels. 


1.  How  much   will  5630  lb.  of  ginger -come  to  at  9  piastres 
per  100  ? 

5630 
9 


506170 
20 


14  |0d  Ans.  506  piast.  14  sol. 

2.  What  will  9760  lb.  of  pepper   come  to^  at   271  tlucat* 
per  100? 

5760 
27i 


68320 
I90QO 
2440 

J)20o^6a 

44326'f 


piast.     310;<:|86f 
20 

soldi      17i33^ 
J  2 

^cn.     4100         Aqs.  3102  piast  I7s0l.  4  deft< 


192  EXCHANGE. 

3.     Wliat  will  143700  lb.  of  pitch  come  to,  at  26  paiils 
per  100  ? 

NoTi;.     1  paul  is  equal  to  |  of  a  livrc. 

14370G 
26 


852200 
287400 


37362,00  pauls. 
2 

3)74724 

j6)  24908  livres. 

4151  6  8 

Ans.  4151  piast.  6  sol.  8  dei, 

4.  How  much  will  4200  sacks  of  wheat  come  to,  at  .26li>TOfi^ 
<ftbctive  money,  per  sack  ? 

4200 
26 


25200 
8400 


Uv.         jnase. 

^     :     I       ::       109200  livres. 

Ans.  18991  piast.  6  sol.  1  den* 


piast.    s.  d. 

S^.  100  ban-els  pork  • .  16  piastres  per  barrel*  •  • .  •  •   1600     0  0 

6.  1000     do.     flour  . .  lOi     do.     10500     0  0 

7.  2660  lb.  coflPee 26       do.  per  100 691   12  0 

8.  6578  lb.  pimento..  18       do.     do. 1184     0  9 

9.  9370  lb.  rice 24  liv.  cur.  money  per  100   •  -374  16  0 

10.  97270  lb.  logwood  •  •  16  piastres  per  1000   1.556     6  4 

11.  4170  lb.  Russia  wax  33i  ducats  per  100 1629  15  6 

12.  104060  lb.  su<iar 30  piastres  per  151  lb. 20674     3  5 

13.  3350  lb.  loaf  sugar  30     do.      per  100 1005     0  0 

14.  1000  casks  tar 4|  do.       per  cask 4500     0  0 

15.  100000  Stare*.. ^^..  4    do.      per  100. ..  ^.j^.  4000    0  9 


EXCHANGE.     •  193 

K  A  r  L  E  S. 

Accounts  arc  kept  in  Ducats  and  Grains,  reckoning  TOO 
grains  to  1  ducat. 

The  current  coins  are  grains,  carlins,  ducats,  dollars,  and 
ounces. 

lOgrainsmake  1  carlin  ;  10  carlins  1  ducat;  3 ducats  1  ounce. 

The  Naples  dollar  passes  for  120  grains,  and  the  Spauibli 
dollar  for  1^6  grains. 

100  lb.  Naples  weight  are  equal  to  ()4§  lb.  English. 

Brandy  is  sold  per  cask  of  12  barrels,  or  132  gallons  ;  Cd 
karafts  make  a  barrel. 

Sewing  silks  are  sold  per  lb.  of  12  ounces. 

Lustrings  are  sold  ^er  cane  of  84  inches. 

Sugar,  coffee,  iish,  and  tobacco,  are  sold  per  cantar,  of'l^S 
lb.  in  the  United  States.. 

The  cantar  is  subdivicied  into  100  rotolas  of  33  ounces  each. 


1.     What  is  the  amount  of  10  casks  6'  barrels  C9  karafts  ®f 
brandy,  at  ^2  ducats  per  cask  ? 

"  5)2 
10 

Obbls.  I  a6 

20  kar.  1^8  2   55 

5  do.      \  64-  nearest. 

4  do.      \  51 


S)69   70     Ans.  969  ducats,  70  grains. 
5.  What  is  the  amount  of  2  casks  of  clayed  sui^ar,  weighing 
at  10  cantars,  51  rololas,  at  65  dollars  per  caniar  f 


VJt. 

dch. 

rot. 

100      ; 

:     05   : 

:      1051 
65 

due.     683,15 


Or  thus 

? 

65 
10 

650 

50 

rot. 

1 

o2 

50 

1  ( 

due. 

05 

683 

15 

Ans. 
II 

683  ducats, 

15 

grains. 

194.  EXCHANGE. 

3.  How  much  is  the  amount  of  1  box  of  scented  soap,  con- 
taining 100  parcels  of  16'  ounces  each,  at  22  grains  per  rotola? 

100 
16^ 

i»2.  gr.  

33     :    22     ::      1000  or.     :     Ans.  10  ducats,  66  grains. 

4,  What  is  the  commission  on  9g6  ducats,  at  2  per  cent. 

Ans.  19  ducats,  92  grains. 
can.  rot.  ducats.  due.  ^r* 

5.  3  73  of  coffee  ••••......  -73  per  cantar..     272  29 

6.  l6'l9|soap.. 21    340   14 

7.  1   59    do.     » 21    *. 33   39 

8.  7  97^  do.     21 167   52 

9.  67i  scented  ditto 30    • 20  25 

10.  52     white  ditto    *......    17 8   84 

11.  7  64     raisins    12    91   68 

12.  2  casks  llbbls.4kar.ofbrandy  102     per  cask  ••     298  06 

13.    10  do.  43  do.      ditto*.   92      do. 82    I6 

14.    9  do.  12  do.     ditto..    92     do. 70   53 

Ij,  355  canes  of  silk    2  50  per  cane    887  50 


TRIESTE, 

Accounts  are  kept  in  Florins  and  Krcutzers. 
60  krcutzers  make  1  florin. 

The  exchange  on  London,  (1st  May,  180o^)  was  12-  flprif}!  for  the  pouni 
»terling. 

The  other  kinds  of  money  are  Soldi  and  Livres. 

20  soldi make 1  livre. 

5|:  livres » 1  florin. 

100  U>.  of  Vienna  are  equal  to  123  lb.  Enghsh. 
A  barrel  of  wine  is  equal  to  18  gallons. 
A  brace  of  Trieste  is  equal  to  J  of  a  yard  English. 

A  staro  of  wheat  is  2|-  bushels  nearly — 3-|  siaros  is  equal  to  an  Engli'  li  quar- 
iicr  of  8  bushels. 

The  tares  on  articles  of  Colonial  produce,  are 

Sugars  in  Brazil  large  cases     271  lbs.  of  Vienna 
middle  sized  do.  244  per  Case 

small  do.   217  do. 
llavannah  boxes      .50  do. 

hogsheads     14  per  cent. 
Coffee,  Cocoa,  pepper,  ^:c.  arc  enij)tied,  and  ihc  package  welgl.ed. 
ICo  (ares  or  allowances  are  made  on  d\ewood3. 

Sales  arc  made  for  bilk  on  Vienna  at  3  nioulhs  date,  and  remittances  genet- 
ally  made  thiou^h  the  baaLcrs  of  that  place, 


EXCHANGE.  ^9^ 

1.     ^Vhat  Is   the  amount  of  263  lb.  Vienna  \veiglit  of  soap, 


at  22  kreutzcrs  per  lb.  ? 

263 
22 

5  26 
526 

610)57  8K^ 

96  26  Ans.  96  dor.  26  kreutzers-. 

2.     758  gallons  wine,  at  21  florins  30  krcutzcrs  per  barrel  ? 
758 
21 

758 
1516 
30  kr.     J         379 

18)16297(905 
162 

"^ 
90' 

7 
60 

18)420(23 
36 

"~6o 

54 

6  Ans.  905  fl.  23j  kr.  " 

Jl.  hr.  fi-      kr. 

3:  120  stares  of  wheat  at  4  20  per  staro.  Ans.  520  00 
4.  715  braces  of  silk  •  •  •  •  3  50  per  brace.  •  •  •  •  2740  50 
.5.   1730  lb.  coffee    58  per  lb. l672  20 


i^^  EXCHANGE. 

PJLEiaiO  IN  SICILY. 

Accounts  arc  kept  in  Onzcs,  Tarins  and  Grains. 

50  Grains make 1  Tai  in. 

30  Taiins    • ...*#   1  Onze  or  Once. 

i'eb.  3,  IS03,  the  value  of  the  money  of  Palermo  in  United 
States  cuiiency  was  as  follows  : 

1  Grain equal  to 4  Mills. 

'20     do.    HZ      1  Tarin =z 8  Cents. 

210     do.    =r    12     do.nl    Sc.  dollar.  •  in.  •      90     do. 
600     do.    —   30     do.  —  2l  do.  —  1  Onze  =  240     do. 

The  Spanish  dollar  is  current  at  25'2  grains.  The  value  of 
the  onze  at  par  is  11^.  3(1.  sterling,  'i  he  exchange  on  London 
Feb.  3,  \'j>03,  was  56  tarina  for  the  £,  bterliiig,  or  10is\  3|c/» 
sterling  per  onze. 

The  Cantar  of  Sicily     rr      176  lb.  Avoirdupois. 

The  llottoli zz  l|lb.         do. 

100  llottoli  make  a  Cantar. 

A  Cantar  of  Oil  is  25  gallons  English  measure.  The  Sici- 
lian barrel  contains  9  gallons. 

Mahogany  is  sold  by  weight  ;  one  foot  board  measure  will 
1^'eigh  about  2  rottoli. 

The  measure  called  Caffis  is  3|  gallons. 
The  lb.  in  Sicily  is  12  oz.  avoirdupois. 
The  Saiin  is  485  lb.  avoirdupois.' 


Examples. 

1.   What  cost  264  Cantars  25  rottoli  of  Mahogany  at  8  oii- 
^C5  15  tarins  per  cantar  ? 

2(S4     • 
8 


2112 
15  tar.  J  =:  132 
25  rot.  I  zz:  2  3   15 


52246*  3   15 

Als.  2246  onz.  3  tar.  15  z^* 


EXCHANGE.  197 

2.  A  cargo  consisting  of  356'4  quintals  of  Fish  invoiced  at  5 
dels.  50  cts.  per  quintal,  is  sold  in  Palermo  at  75  per  cent,  ad- 
vance ;  what  sum  must  be  received  for  it  at  252  grains  pep^ 
dollar  ? 

3564^ 
5 

17820 
50  cts.  J  zz      1782 


19602 
50  perct.  |  =:  5)801 
25 I  z=     4000  50 


dols.  34303  50 
252 


6S<)06 
171515 

6S605 


2|0)86'444S|2  grains. - 

3lO)43222|4  2 

14407   14  2 

Ans.  14407  onx.  14  tar.  2  gr^- 

3.  What  is  the  Brokerage  on  13  Ul  onz.    12  tar.   at    1 J  per 
eent.  ? 

13131   12 
1 

13131    12 
I  =    1641    12    15 

147172   24   15 
30 

21184 
20 


R2 


16'|<}5 

x\ns.  147  0112.  21  tar.  l6  gi\ 


l^S  EXCHANGE.  • 

GENU  A. 

Accounts  are  kept  in  Denarii,  Soldi,  and  Pczzos  or  Lire?. 

12  denarii nuike 1  soldi.. 

20  soldi  . .  • . 1  pezzo  or  lire. 

1  pezzo  of  exchange 5 1  iires. 

The  course  of  exchange  is  various — from  47<:/.  to  58c/.  ster- 
ling per  pezzo  or  lire. 

in  Milan,  1  crown     rz      80  soldi  of  Genoa. 

•  •Naples,         1   ducat      zn      85  do. 

•  •  Leghorn,      1  piastre    n:      20  do. 

•  •  Sicily,  1  crown     zz   127  3       ^^• 

To  reduce  Exchange  money  to  Lire  money. 
Rule.    ^Multiply   the  exchar'ge  money  by  5|  for  lire   mo- 

Ex.l^iJ^LE. 

In  384*  pezzos  of  exchange  how  many  Iires  ? 
384 


1C)'20 

\ 

192 

\ 

})6- 

220S  Ans.  2:CS  Iires. 

To  reduce  Lire  money  to  Exchange, 

Rule.     i\Iultiply  the  lire    money  by  4  and  divide  the  pr«- 
•  .',(  i  i^y. 23  for  exchange. 

Example. 

In.  2208  Iires  how  many  pezzos  of  exchange  ? 
2208 

4 


23)883:.  ■ 

1.93 
184 


—  Ans.  384  pezzos  of  exchange. 


^   EXCHANGE.  199 

To  reduce  Lives  to  Sterling. 

Rule.  Asl  lire  is  to  the  rate  of  exchange  so  is  the  lircs  to 
the  sterling  required. 

Example.. 

In  3()0  lires   how   much  sterling,   exchange  at  54c?.  sterling 
per  lire  ? 

/.  d.  L 

1      :      54      ::      3(50 

54» 

1440 
1800 


12)19440 


2,0)16'2|0 

£.81  Ans..€.81  0  0  sterl. 


V  E  N  I  C  E. 

Venice  has  three  kinds  of  money,  viz.  Banco  money,  Banco 
current  money,  and  Picoli  money.  Banco  nmney  is  20  per  ct. 
better  than  banco  current,  and  banco  current  20  per  ct,  bettey 
than  picoli. 

The  different  denominations  of  money  are  Denari,  Soldi^ 
Grosi.  and  Ducats. 

12  rienari,  or  deniers  d'or,  make   1  Soldi,  or  sol  d'or. 

5  J  soldi  ••• 1  gros,  or  grosi. 

24  gros,  or  grosi 1  ducat. 

100  ducats  banco  of    Venice  in  Leghorn  rz  ^3  pezzos. 

Home  zz.  6'8i  crowns, 

Lucca  zz  77     do. 

•  • '  • Frankfort  zz  1 39|  florins. 

The  par  of  exchange  in  1793  was  oO^r/.  stciling  per  ducat 
Ijaiicu. 


eoO  EXCHANGE. 

Example. 

IIow  much  sterling  is  equal  to  '2712  ducats  banco,  exchange- 
at  50^(1,  steilmg  per  ducat  banco  ? 

due.  d.  due. 

1     :     50i     ::     2712' 
4.  201 


201  2712 

54240 


4)545112  farth. 
12)13b"278pence. 
2lO)lIS5|6  6  shills. 
Ans.  £.567  l6  6  sterling. 


S  M  Y  R  N  J. 

Accounts  are  kept  in  piastres  and  hundredths,  except  the 
Knglish  accounts,  which  from  ancient  custom  are  kept  in  pias- 
tres and  eightieths  or  half  paras. 

The  fractional  parts  are  sometimes  called  aspers,  100  aspers 
to  1  piastre. 

The  foiiowing  calculations  are  made  in  piastres  and  hun- 
dredths. 

A  piastre  is  equal  to  40  paras,  and  a  Spanish  dollar  to  136 
paras. 

340  piastres  are  equal  to  100  Spanish  dollars. 
The  exchange  on  London  was  13  piastres  for  1  pound  ster- 
ling, J\iay  ]4th,  1800. 

Their  -weights  are  the  Rotola,   Oke,  Cheque  and  Tiffee — 

A  rotola u;arked  Ho.  is  180  drams. 

An  oke Y^  is  400  do. 

A  cheque  of  opium  •  •  •  • is  250  do. 

do    of  goal's  wool is  800  do.  or  2  okes. 

A  tiiiee  of  silk  • is  6*10   do. 

100  rotolas,  or  1800  drams,  or  45    okes  are  a  quintal  of  this 

country. 
112  lb.  Lnglish  should  render  here  40:|  okes,  or  5)0^  rotolas, 

43  okes  of  this  country  render  l2o^  lb.  Lnglish. 
A  pike  is  27  incUcsi  nearly. 


EXCHANGE.  201 

To  change  piastres  to  dollars, 
Ru  Li:.     Mulnply  the  piastres  by  5,  and  divide  the  product 
by  17,  tor  cents. 

Example. 
Change  1277 Mq  piastres  to  dollars. 
1277,53 


17)G387,75(375;75 
51 

123 

iiy 

85 

127 
119 

85 

85         Ang.  575  dols,  7o  cts, 

7'o  change  dollars  to  piastres, 
Rule.     Multiply  the  dollars  by3f  tor  piastres. 

Example. 
Change  375  dollars  75  cents  to  piastres. 
S75J5 
H 


1127,25 


Ans.     1277,55  piastres. 


Practical  Questions. 

1.     Plow  much  will  10  serons  of  cochineal  come  to,  ^veigh• 
in^  neat  724-  okes  73  rotolas,  at  $0  piastres  per  oke  ? 
724,73 
80 

Ans.  57978,40  piastres. 


205  EXCHANGE. 

2.     299  l^ags  of  sugar,  weighing  506   quintals  q6   rotolas, 
tare  14  rotolas  per  bag,  at  110  piastres  per  quintal, 
gross    506  96  239 

tare        41   «5  14 


neat    465   10  1196 

110  299 


Ans.  511(31   OOpiast.  100)4186 

41   S6 
3.     4  cases  of  opium,  weighing  gross  1026   rotolas,  tare  84 
•kes  75  rotolas,  at  10^  piastres  per  cheque. 

Kofc,  1  rotola  is  equal  to  /^3  of  an  oke,  and  I  oke  to  if  chequO* 
rot.       1026 
9 

20)9234  rot. 

gross  okes     46l  70 
tare         84  75 


okes    376  95 
If 

S76  95 
3 

S76  95 
226   17 

5)1130  85 
226  17 

cheques  603  12 
10| 

6031  20 
301  56 
150  78 

Ans,  piast,  6483  54 

4.     893  pieces  of  copper,  neat  okes  19743,85,  at  |o    ^^  70 
paras  per  oke.  0.  R, 

19743,85 
70 


4J0)  1382069510 
Ans.  piast.  34551,73 


EXCHANGE.  203 

5.    What  is  the  custom -house  duty  on  1 974-0  okes  of  copper 
at  H  amo  2^  per  cent.  ? 
Note.  The  chargejs  are  all  established  by  a  tariff  of  the  Levant  Companj. 

15>740 

^ 

39480 
9870 


4|0)4935iO 


agio  2j  =1  4-0)  1233,75  amount  of  duty  at  2|  paras. 
30,84  agio  at  2^  per  cent. 

Ans.  piast.  1264,59 

6.     English  consulage  on  430  quintals,  at  51  piast.  agio   7 
per  cent, 

430 
H 

2150 
215 


2365 
7 


An?,  piast.   165,55 

7.     Custom-house  duties  on  88  quintals  9O  rotolas,   at  J^% 
.iigio  2|  per  cent. 

88,90 
20 


n|o)i7780io 

,40 


Ans.  piast.  l6,5^' 


IB*  EXCHANGE.     ^ 

^  8.  What  will  the  follow! nij;  charges  amount  to,  \]2,  porterac^e 
4*0*  hoube  porters  ^%,  weighing  /(^,  chan  duty  /y,  visiting  and 
marketing  /^  per  quintal  on  438  quintals  r 

porterage-...    8  433 

house  porters     4  _  -^ 

weighing o  ' 


chan  duty. 


..'1  4|G)  74416 

17  Ans.  piast.     1SG,15 


ENG  LISH  WEST-INDIES. 

Accounts  are  kept  in  Pounds,  Shillings,  and  Pence. 

JAMAICA  A  N  D  BERMUDAS, 

The  Spanish  dollar  passes  at  6s.  ScL  ;  3  dollars  are  equal  to 
20  shillings,  or  J  pound,  Jamaica  currency. 

To  change  Jamaica  currency  to  Federal. 
Rule.      Multiply  the  pounds  by  3  tor  dollars.      If  there  be 
shillings,  &c,  increase  the  pence  in  the  given  sum  by  \  for  cents. 

Examples. 

1.     When  lumber  is  sold  in  Jamaica   at  ^.15  per  M.  how 
much  is  it  in  Federal  money  ? 

15 
3 

Ans.    4-5  dols. 
Ht,     Change  ^.54  125.  lid,  Jamaica  currency  to  Federal, 


54 
20 

12 

cts-, 

11 

1692 
12 

i)131l5 

327  8  J; 

AiiSc  iQo  dols.  SH  ^^- 


EXCHANGK.  505 

What  wilH02,896feet  of  boaids  come  to,  at  £.15  per  M.i 

102,896 
15 


514480 
102896 

£.1543,440 

20 


s.   8,800 
12 


d.  9,600  Ans.£.1543  8  9 

4.     What  will  5  hhds.  of  sugar  come  to,  weighing  8519  l^* 
neat,  at  70  shillings  per  100  lb.  ? 

8519 
70 


.        2lO)596|3,30 
Ans.  £.298  3  3 

5.  How  much  will  5  hhds.  of  sugar  come  to,  weighing  910^ 
lb.  neat,  at  75  shillings  per  100  lb.  f 

9103 
75 


i  ■ 

,»»;f»  fh?»''^  ■ 

45515 
63721 

2lO)682|7,25 

1 

Ans.  £.341  7  3 

BA  READ  OES, 

The  Spanish  dollar  is  6s,  3d,  Barbadoes  currciicv-, 
S 


20a  EXCHANGE. 

y'o  change  Barhadoes  ciirrcncij  to  Federal, 
iPwULE.     Increase  the  pcnc-e  in  the  given  sum  by  J  for  ccnt^ 

Example. 
Change  <£.49   l^s^   10c/.   Barbadoes  money  to  Federal. 

Proof  I)  1586.9  J  cents. 

£.49  11  10  3967I 

20  

12)  11902  pence 


991 


12  2;0)99ll      10 


101b902  ^.49    11    If) 

3967} 


158, 69 J  Ans.  158  dols.  6^1  ccn4». 

Other  calculations.asin  Jamaica^ 


31 ARTIXICO,  TOBAGO,  a^d  ^7\  CHRISTOPBERS. 

These  islands  being  inhabited  by  French  and  English,  the 
former  keep  their  accounts  in  I..ivres,8oIs,  and  Deniers,  and  the 
latter  in  Pounds,  Shillings,  and  Pence. 

A  current  dollar  is  8^.  3d,  \ 

A  round  dollar  passes  for     ^s. 

When  payment  of  freight  or  goods  is  mentioned  in  Spjinish  dollars,  di5a- 
greement  respecting  their  vahic  has  frequently  arisen  ;  and  to  [)reveni  it,  some 
persons  distinguish  them  by  round  and  cinrait  dolhirs  ;  others  ni.ention  the 
bitsio  each.  But  the  most  certain  \vay  is  to  specify  the  number  of  sliiilings 
or  livres,  instead  of  dollars  ;  tlius,  A  sells  to  13  a  barrel  of  flour,  a(  SI' sliiilings 
or  livres  ;  in  pnynjent  Bmay  allow  him  11  dollars  at  9  shillings  each,  cr  12  , 
dollars  at  86.  3c/.  each,  cillicr  being  equal  to  S'9  shillings  or  livres,  the  turn  \ 
i-pccilied  by  ihch'  a^ieemcnt^ 


'exchange.  mr 

FRENCH  WEST-INDIES. 

Accounts  are  kept  in  Livres,  Sols,  and  Deniers. 

12  deniers  make  1  sol,  and  20  sols  1  livre. 

The  Spanish  dollar  passes  in  some  places  for  8  livr<)S  5  sols, 
and  in  othci-s  for  9  livres. 

1  cwt.  or  112  lb.  in  the  U.  Staties  is  equal  to  104- lb.  French. 

100  lb.  French  are  equal  to  108  lb.  nearly,  in  the  U.  States, 
When  any  commodity  is  to  be  marked  in  French  weight  4  per  cent,  is  added 
to  the  neat  hundreds  ;  thus  a  hogshead  of  fisli  wcighingneat  10  cwt.  is  marked 
10401b.  Fish  shipped  from  the  United  States  will  answer  to  the  weight  thus 
marked,  provided  it  comes  out  in  good  order,  and  the  cask  weighs  exactly  the 
customary  tare,  which  is  10  per  cent. 

100  lb.  of  coftee  or  cotton,  bought  in  the  French  islands, 
vill,  or  ought  to  weigh  108  lb.  (it  will  often  weigh  110  lb.)  in 
the  United  States  ;  and  as  these  articles  are  sold  here  per  lb. 
there  is  a  gain  of  8  to  10  per  cent,  in  the  weight.  But  on  su- 
gar, which  is  bought  for  lOOlb.  and  sold  here  per  112,  there  is 
a  loss  of  6  per  cent,  because  there  is  4  per  cent,  between  the 
American  cwt.  and  100  lb.  French,  and  2  per  cent,  difference 
in  the  tare.  The  tare  on  brown  sugar  in  the  P^rench  islands 
being  10  per  cent,  and  the  American  tare  12  per  cwt.  Th« 
loss  on  cla3^ed  sugar  is  greater,  occasionediJjy  the  customary 
tare,  which  is  but  7  per  cent,  in  the  French  islands,  whereas 
it  is  here  12  per  cent,  the  same  as  on  brown  sugar. 

Note.  The  tare  allowed  on  sugar  among  niercliants  is  1?  per  112  ;  that 
allowed  by  the  custom-house  is  12  per  100.     [.SVe  Tare  and  Tret,  page  9o.] 


1-     Change  10^92  livres  to  dollars,  at  8|  livres  per  dollar. 

Si      10692 

4  4 


'J^3   )      427()8(129ff 
33 

97 
66 


3\6 

198 

li)8  Ara.lQ^dijm 


^08  EXCHANGE. 

x\     Chano^e  7713  livres  to  dollars,  at  g  livres  per  dollar. 
9)7713 


Ans.     S57     dollars. 
5.     In  IQgS  dollars,  at  S|  livres  each,  how  many  livres  ? 

H 

10368 


Ans.    10(H)2  livres* 

4.  S57  dollars,  at  9  livres  each,  how  many  livres  ? 

Ans.   7/  io  iivn«. 

5.  What  will  l642  lb.  of  coife©  come  .to  at'lcl  sols  per  ll^.'l 

15 


8210 
I()42 


.!!?|0)240'310  sols. 

livres   1231    10  Ans.  1231  Jiv.  10  sols. 

6,     17  SO  ib.  cotton  at  157  livres  10  sols  per  ICO  lb. 
1780 
157 


12460 
8(,'00 
1780 
10  sols.      J  8<]0 


liv.     2803150 
20 


sols     lOlOO  Ans.  2S03  liv.  10  sols. 


EXCIIANCE.  ^ 

y.     24  barrels  of  beef  at  101  liv.  I  sol  3  den.  per  barrel. 

Uv.     s,     d. 
101      1     3 
6 


Go6    7    6 

4 


2425   10     0'     Ans.  2425  liv.  10  sols. 

S.     How  many  dollars,  at  8  livres  5  sols  |x?r  dol.  will  }3^for 
l^hhds.of  brownsugar/wdghing  133^5  Ib.at  40 liv.  per  100 lb;? 

1336^5 
40 


8J   534(),00 
4  4 

33)21384(648  doK- 

J  98  in 

158 
152 

"264 

2^4^  Ans.  C48dols. 

9.  A  cargo,  amounting  to  12536  dels,  in  the  United  States  ir. 
Sold  at  12^  per  cent,  advance  on  the  invoice  ;  how  many  livrea 
will  it  amount  to,  estimating  the  dollar  at  8|  livres  each  ? 
12|~^)  12536  invoice. 
1567  advance. 


14103  amount. 

8 


112824  livres  at  8  per  dollar. 
«  sols     J       3525| 

Ans.  Il6349:|  livres  at  S^  per  dollar. 
Si? 


eiO  EXCHANGE. 

safe.  d. 

10.  6  hlids.  coflTee,  weighing  4471  lb.  at  14     6  per  lb.  • . 

11.  14  do.    siigas  do. 16477 58  liv.  per  100 

12.  1  bale  ol"  cotton,   do.    ••    ^^i'7«  •  •  •  150  . . .  •  do.  .. 

13.  94  hhds.  fish,  . .   do.     101313 33    ...do... 

14.  16  cajbks  of  rice,    do.  ..    6575- •••    40  lO.-do.  -. 

15.  1390  hoops 480 per  M. 

16.  1.5059  feetof  boar  Js ^ 100-    ..    do.-... 

17.  48  shaken  hhds.  wilh  heads-  • ' 7   15  per  Iihd. 

1 3.  29  barrelsof  beef 90  15  j)cr   bbJ. 

1 9.       6759  veits  ef  molasses 2fr  per  veit 

%0.  32070  gills,  do.  at  7  31 7«.9d.  per  tierce  of  60  gals.   .... 


SPANISH  W£ST-INDIES.- 

Accounts  are  kept  in  Havanna,  La<:;uiia,  Vera  Cruz,  he,   in^ 
dulhirs  and  reals,' reckoning  8  reals  to  a  dollar. 
The^'Spanisharobe  is  26  ib. 

1.  vWiiat  will  123  pieces  Bretagnes  come  to^  at  26'  reals  per- 

piece  ? 


f3?. 

.1. 

d,^ 

3241 

9 

6 

61261 

5 

2 

340 

10 

0 

33433 

5 

9 

266^2 

17 

6 

6G7 

4 

0 

1505 

18 

0 

37'-2 

0 

0 

2631 

15 

0 

87^6 

1<* 

0 

399.)  t) 

9 

;o 

8)3iy8 


3^9  ^       Ans.'spp  dols.  G  led^ 

5.     2178-i  feet  boards,  at  45  dollars  per  thousandv 
21784 

45  per  M, 


108920 

87136'  - 

'  "'■    '■>■■■ 

9S0J'.28O 

8 


?|^40  Ans.  080  clois.  2  reals. 


EXGHANGX.  ^l 

5,     153  cases  of  gu^  At  §§  dpllq^rs  per.  case. 

1224 
2  dp.     .38  2 

Ip3j8^.^      Aus.;1338,dols,  ^Teafe. 

-  •-.  ,  ,'  ,»^ 

4.,  \Yihat  is-^,  ppmmi^io.n  ;pfi  •14^^9)^^dftUa]|?  3  rieals,  ,^t  4j 
percent.?      .-i-,- ^  ^ ;  v  i  ■•  «!i  :;■■<■>»  •    •  .,•  v,  ..i.  ,  .  .  .     '.  .-   .. 

14792  5 

mhvnm  X  •' .   i  :  ''^iLi 

59H70  4'" 
8 

5l(},4,  Ans,  591  dbls.  5rcals.  ^ 

5.  What\vill42  bbls.  of  white  sugar  come  to,  weighinggross 
415  arobes  18  lb.  tare  and* tret  on  the  whole  858  ib,  at  26'  reals 
per  arobe  ?  a/\    ,Z/>.  '/ 

415    18 
858  lb.  make      34     8 

381    10 

26' 

2286 
762    -  ■ 
IGlb.nJarube       10 

8)9916  reals.  '■ •  .-^ 

^ — —  -^Ot  9ffi0}  'tl.      * 

1239  4.         Ai\s.  1239  dols.  4  reals/ 

duh.    rcal.f. 

(j,  125  pieces  bretagncs  at  26  reals  •  .•  • 406  2 

7.  500    do.    ••    do.....  24|  do.  ••..  ......    1^31  2 

S.  SO  umbrellas  .•••••  (j A  dollars     ......     ^20  0- 

9.  1 47  arobes  of  butter  ..  2^^    (\o.  per  100  lb.  ^918  6 

10.  2405  arobes  I9lb.  sug:ii  2^  reals  pei^^^Aroby    ^  ^^518  0 

11.  I66O    do.. .12. .do.  .^  21,  do,..^-do.    -V^  3-358  7 
:2.  lW9^,fe]e^:Jj9a|Hh?    ....  4P,:d(^.^.^er  M.  ..       667  ^ 


iit  EXCHANGE.  . 

1 

EAST-INDIES. 

C  A  L  C  U  T  T  J. 

Accounts  are  kept  in  Rupees,  Annas,  and  Vice* 

12  pice  make  1  anna,  16  annas  1  rupee. 

By  the  bazar,  or  market  exchange,  for  June,  1797,  the  efC-p. 
ghan^e  was,  viz. — 

106  English  guineas  were  equal  to  956  rupees  4  annas,- 
100  Spanish  tioliars  were  equal  to  212  rupees. 

In  weights — 16  chittacks  make  1  seer,  40  seers  1  maud. 

The  factory  maud  is  7^  lb,  English. 
The  bazar  maud   is  84      ditto. 
The  imports  are  sold  by  the  factory  maud  and  current  rupees. 
The  exports  are  bouglit  by  the  bazar   maud  and  sicca  rupees* 
100  sicca  rupees  are  equal  to  ll6  current  rupees. 
Bednah,  tin-plates,  and  hides,  are  sold  percorge,  20toacorge. 
The  cavid  is  half  a  yard  English. 


l..Wliat  will  3905  dry  hides  amount  to,  at  12  rupees  percorge? 
h.  r.  h. 

20     ;     12     ::     3905 
12 


2|0)4680lO 

2343  Ans.  2343  rupees. 

2.  How  much  will  189  bazar  mauds  oi  seers  8  chittacks- ©i 
sugar  come  to,  at  6  rupees  per  maud  ? 
189  31   8 
6 


■w 

11 

34 

20  seers 

h 

3 

10 

h 

1      8 

1 

A 

0     2 

4 

S^chit. 

4 

m 

0      1 

n 

11 

38   11 

6 

Ans,  nSSr.  lU.  ft^.- 


EXCHANGE.  '    -h^ 

BOM  B  A  Y. 

Accounts  are  kept  in  Rupees,  Quarters,  and  Rees. 
100  rees  make  1  quarter  ;  4  (]uarters  I  rupee. 
?>ii;  2  ISrCupees  were  equal  to  lOOSpAnisli  dollars,  iji  April,  1800. 
'  The  current  money  is  ift  Mohurs,  Rupees,  and  Pice. 
50  pice  nurke  1  rupee  ;   15  rupees  1  mohur. 

The.wG^ghtfe  are  pounds,  mauds,  ajid  candies  ;  the  pound  t^ 
same  as  English. 

A  Bombay  maud  is  28  lb. 

A  Surat  maud  is  o7 }^  lb. 

21  Surat  mauds  or  78-1  lb.  make  1  Surat  candy. 

Cotton  14 -sold  by  the  Surat  candy. 

{'iiinphirc  and  M©cha  cotlee  are  sold  by  the  Surat  maud. 

Malabar  pepper  is  feold  by  the  Bombay  *caiidy  of  a88  ib» 


In  274  bales  of  cotton,  weigliing  neat  996  cwt.  2  qrs.  23  lb. 
how  many  Surat  candies  ? 

784lb.ii:7cwt.  7)99^     2     23 

142     200  two  hundreds. 

24  excess  12  per  cent. 
56  twa  quarters, 
23 

303  Ans.  142  can.  3031b. 


MA  D  R  A  S. 

Accounts  are  kept  in  Pagodas,  Ei^nams,  and  Cash. 
80  cash  make  1  fanam  ;  SG  fanams  1  pagoda. 

The  Spanish  dollars  were  in  1793  and  \Qf),  at  l6'j  dollars  for 
100  star  pagodas  ;  making  the  paga4*  worth  16'5  cents.  I'he 
revenue  laws  of  the  United  States  reckon  them  at  184  cents. 

The  Bengal,  or  Sicca  (new)  rupee  is  worth  46  to  47  cents. 
The  revenue  laws  of  the-United  "&nit<:s  vaKie  ttiem  at  50  cents. 


214  EXCHANGE. 

The  current  exchange  is  340  Sicca  rupee?!,  for  100  Star  pa- 
godas. 

A  Lack  of  rupees  is  100,000. 

Cowries  are  sea  shells  used  as  small  money  in  India,  and  on 
.  the  coast  of  Africa,  to  make  change  among  the  natives  in  the 
bazar,  or  market,  and  in  payment  to  the  coolies  or  labourers. 
In  May,  179-?-^  rupeewas  worth  5120  cowries.  The  common 
cowries  are  generally  at  5  t©  7  rupees  per  Bazar  maud,  the  bet- 
ter sort  from  10  to  14  rupees  per  maud,  the  price  varying  ac- 
cording to  the  kind. 

The  piculis  133  J  lb.  English. 

100  cattas  make  a  picul. 

A  maud  is  25  lb.  Troy,  20  mauds  make  1  candy. 

The  excellence  of  their  cloth  is  defined  by  the  t/ireada  in  the 
warp. 

The  duty  payable  at  the  cu&tom-house  is  2 J  per  cent,  out-  - 
wards  and  inwards.  This  is  taken  on  imports  according  toth#- 
invoice,  and  on  exports  at  the  actual  co&tat  the  bazar  or  market. 


B  A  T  A  V  I  A. 

Accounts  arc  kept  in  Rix  Dollars  and  Stivers. 
The.rix  dollar         is  48  stivers. 
The  ducatoon         is  80  do. 
The  Spanish  dollar  is  6*4  ditto;  sometimes  it  passes  at  60  stiv*. 

125  lb.  Dutch  are  equal  t©  133 J  lb.  English. 

3  25  do.  make  1  picul. 

100  cattas 1  ditto. 


In  1333  rix  dols.  \6  stiversjhow  many  ducatoonsr 
1333     l6 
48 

10670 
5333 


>|0)6400|0 


Ans.    800  Jucatooni.. 


EXCHANGE.  ^li 

2.     Wliat  will  127477  cattas  of  bar  iron  c6mc  to,  at  9  t«S 
dollars  per  picul  ? 

cat.       r.d.  cat. 

As  100  :  9  '•'  1^7^77 
9 


11472,93 
48 


744 
372 

44,64      Alls.  11472  r.  dols.  44  st, 

3.     What  will  3894  bottles  of  wine  come  to,  at  36  stiver* 

'per  bottle  f 

3894  Or  thus,  36  stiv.ziS  rix  dol. 

3894 


24  s 
12 

tiv. 

i 

19-^7 
973  24 

*) 

3 

1  ^f^9,^ 

2520  24 

I  1  wo  -* 

2920  24 

Ans 

.  2920 

rix 

(lols.  24  stivcrf* 

L  In 

3 1478  lb 
12 

.  ofsucjar,  how 
5)31478(251 
250 

many  \ 

)icul 

s? 

647 

625 

228 
125 

103  Ans.  251  piculs  103  lb, 

pic.     Pfs 

5.  In  50632  lb.  how  many  piculs  ?  Ans  405     7 

6,  1264s •••... 101  23 


^5=1- 

1953 
139  24 
1   24 

2094  00 

:.T.  .  Wliat  \vilf279  piculb  25  lb.  of  siigar  come  t6y'ii^7|'nx 
dollars  per  picul  ?  ;'  • 

279 

71 


Ans.  2094  rix  dols. 


CHINA,  ^ 

Calculations  are  made  in  Tales,  Mace,  Candareens,  and  Cash. 

1 0  cash  •••••.  make 1  candarcen, 

10  candareens  •  •  •  •  • 1  macje. 

1 0  mace 1  tale. 

The  tale  of  Cliina  is  estimated  at  1  dollar  48  cents  in   the 
United  States. 

The  Spanish  dollar  is  current  at  72  candareens. 
AVeights  ar^iii  Tales,  Piculs,  and  Cattas — 

16  talcs  make  1  catta  ;   100  cattas  1  picul. 
A  picul  is  equal  to  ISSj  lb.  English. 
The  cavid  of  China  is  14i^o  inches;  it  is  divided  into  lOparts, 

To  cJiovge  pounds  English  to  Cattas. 
Rule.     Deduct  25  per  cent,  or  one  quarter,  for  cattas. 

Example. 
In  6266s  lb.  English,  how  many  cattas  ? 
J)62668 
15667 


Ans.     47001  cattas. 

To  change  cattas  to  pounds  English, 
IUtlE.     Add  one  ihird  for  pounds  English. 

Example. 
In  47001  cattas,  how  many  lb.  English? 

1)17001 
15667 


Ans.     62668  lb.  English. 


EXCHANGE.  Jtf 

Practical  QuESTioiNS. 

1.  What  is  the  amount  of  308  chests  of  bohea  ten,  \vciohing 
ttcat  1019j6  lb.  at  15  tales  per  picul  ? 
4)101956' lb. 
25489 


cat.  tal.  » 

100    :     15   ;:     7^467  cattas. 
15 


382335 
7()4G7 


1 1470,05         Ans.  1 1470  tales  5  cand. 

2.     What  will  7^  chests  of  souchong  tea  come  t©,  weighing 
»^at  4875  lb.  at  44  tales  per  picul  ? 
i)4S75 
1218| 


o6j6\  cattas. 
44 


14624 
14^24 
11 

1608,75      Ans.  l608  tal.  7  ma.  5  cand. 

5.  How  many  dollars  will  pay  for  an  invoice  of  tea,  amount- 
ing to  6446  talcs  1  mace  6  candareens  ? 
72)6446   1   6(8953 
576 

648 

381 
360 

I  2.l6 
2l6  Ans.  8953  dois. 


218  EXCHANGE. 

M  A  N  I  L  L  J. 

Accounts  are  kept  in  Dollars,  Reals,  and  Quartos. 

12  quartos  make  1  real  ;  S  reals  1  dollar. 

The  arobe  is  25  lb.    51  arobes  make  1  picul. 
Their  100  lb.  is  equal  to  104^  lb.  English. 


1.     What  will  1897  bags  of  sugar  amount  to,  weighing  neat 
1:^61  piculs  1  arobe  17^  it),  at  6'  dollars  per  arobe  ? 
136T   1   17^ 
6 


8166' 

1  ar. 
12J  lb. 
5 

i 

i 

X 
s 

1 

n 
li 

8l6"8  0  Ans.  8l68  dollars. 

pic.    ar.  lb.         dol.re.  dol.  re, 

2.  118  bags  of  sugar,  weighing  89   1   22|  at  5  7    Ans.  524  G 

3.  66'3  do.....do. 469  3   IS   ••   6       ....2819 


COLUMBO,  ISLE  OF  CEYLON. 

The  money  is  in  paper,  silver,  and  gold. 

Paper  money  is  in  the  bills  of  the  Company,  and  is  of  un- 
certain value. 

Silver  is  in  the  ru;)ees  of  different  parts  of  India. 

The  Sicca  rupee  is  worth  more  than  any  other  by  7  to  8  per 
cent. 

Gold  is  the  Mohur  pagoda. 

The  exchange  is  various,  as  silver  is  rarely  seen. 

6  slivers    *  *  •  •  make  •  *  •  •  1  bhiiliM:.':  Flemibh. 

8  shiPings 1  rix  dollar. 

30  >ti\ers     1  nipoi . 

64  Mo.       ••••    f»»t...  1  Spanish  dollar. 


EXCHANGE, 
JAPAN. 


2l9 


Accounts  arc  in  Tales,  Mace,  and  Candarecns. 

10  candarecns  make  1  mace. 

10  mace •  1  talezz|  of  a  dollar,  or  75  cents. 

Ten  mace  arc  equal  to  1  rix  dollar. 

Six  tales  make  a  corban,  a  gold  coin  not  used  in  accounts. 

In  weights — 10  tales  make  i  mace  ;   l6  mace  1  catta. 
The  ichan  or  hickey  is  3^  feet. 
The  balce  is  65  quarts. 

Thirty-fke  per  cent,  was  the  duty  on  privileged  imports  in  1799.  It  is  on 
the  exports  (which  are  all  free  of  duty)  that  the  Dutch  make  their  prolit  upon 
their  return  to  Batavia.  A  privilege  is  granted  to  ihe  Captain  of  the  Dutch 
shijjsto  carry  money,  which  oi'teii  icils  at  au  advaiico. 


How  much  is  the  neat  proceeds  of  4?  silver  watches,  at  35  ta!ci 
tach,  deducting  the  duty  of  35  per  cent.  ? 
35  tales, 

4 


140 

^5  per  cent* 


7  00 
4C'0 


Sales  140 
Duty    49 


49,00     Ans.  neat  proceeds  91  talts. 


rORM  OF  AN  ACCOUNT  OF  SALFS. 


Dr  III  s. 

Neat. 

talcs. 

talcs. 

tuU's. 

4  -silver  watches,  1st  kind 

o5 

40 

91 

6  silver  watches,  '2i\  kind 

23,1 

48,5,1 

90,0,9 

The  article  is  aiven  in  the  first  column,  the  price  in  the  next 
column,  the  duties  in  the  third,  and  ihc  neat  procccus  in  ihM 
fourih. 


2^0 


EXCHANGE. 


V  A RTI C  U  L A  RS 


0/fhe  To N^- AGE  (/Goods,  as  calculated  to  maJte  np  the  Ton- 
iwgefor  the  Freight  of  Goods,  brought  in  East-India  or  China 
ships  to  Europe — viz. 


Port  St.  George. 


PIECE  GOODS. 


Bengal. 


Pleca  to 

Pieces  tc 

the  Ton. 

the  Ton. 

ALLEIARS 

800 

Elatches 

.     R.80(> 

Belellcs 

400 

Eiiirnerlies 

600 

Callawapores 

800 

Gurrahs 

400 

Chintz  of  all  sorts  • 

• .      R,400 

Ditto,  Jong 

2oa 

Cjinii])ams 

800 

Ginghams,  coloured. 

600 

-Izzurees 

800 

Humhums 

400 

Longcioths 

160 

Habassies 

600 

Moorees 

800 

Ilumhiims,  quilted  •  • 

100 

Salianjpores             • 

400 

Jamdaunies 

8oa 

fcastiacuiidk'S 

.          ..          800 

Jarawars 

600 

Laccowries 

6Q0 

Beng 

AL. 

Lungees  Herba 

800 

Addaties 

700 

Mulmuls 

400 

AliibaUies 

400 

Ditto  handkerchiefs 

400 

Aliachaws 

1200 

Mahamodietei        . .          • 

400 

Aiiibannies 

..      R.800 

Mam'odies 

.     R.40O 

Arras 

..     R400 

Nillaes 

800 

Atcliabannles 

800 

Nainsooks 

400 

Baftaes 

. .      R..400 

Peniascoes 

800 

BandaiinoeSjOr  Taffi 

deFoolas  R.800 

Photacs 

.     R.800 

Carridarrie^j 

600 

Percaulas                 •  • 

800 

C.!iii}):Utifs 

400 

Putcahs 

.      R.40O 

r'oojjces 

600 

Roma  Is 

.      R800 

Cailicocs 

400 

Sannoes 

400 

Chillaes 

600 

Seerbetties 

400 

Cliowiars 

600 

Secrbands 

60O 

(;hundcibannlcs 

800 

Seersuckers 

600 

Chiniiaclmres 

.           ..     R.800 

Scerhaudconnaes    • • 

400 

Cambrics 

. ■      R.400 

Seershauds 

.     R.'K)0 

Chucklaes 

400 

Seerbafts 

400 

Ciishtaes 

800 

Shauibafts 

400 

Cossaes 

400 

Succatoons 

.      R.800 

Charconnacg 

600 

Soosevs 

40O 

Cuttaiintics 

..      R.800 

Sorts 

400 

I)i)()*iO'>rie'i 

. .      R.400 

I'afTcties  of  all  sorts 

.     R.800 

iJiingariea 

. .     R.4-;)0 

Tanjetbs 

400 

Doroiis 

400 

Tcpoys 

.     R.8(,'0 

Dimities 

600 

Terrindams 

400 

Diapers,  broad 

400 

Tains©*k» 

4U# 

Jb^ilto,  uarrovT 

tiUO 

RXCIIANGF.. 


^^\ 


PIECE  GOODS. 


BOMBAV. 


Anna?>atchc8 

Bombay  stiUli 

Byrainpauls  •• 

Bcjutapauts 

Boralchawdcrs  or  brawJs 

Betellce* 

Chelloe-s 

Chiinz  of  nil  sorts  •  • 

Doolies 

Guinea  stuffs,  large 

Ditto,  small 

Longcloths,  whole  pieces 

Ditto,  half  ditto 

Leiiiances 

Musters 

Nurisarees 

Neganepauts 

Niccanees)  large     •  • 

Ditto,  small 

Salaiupores 

Stuffs,  brown 

Tapseils,  larje 

l>itt04  small 


ritcis  to 

ila  Ton. 

.      II 400 

.      ]l.40() 

400 

.    rv.4oo 

1200. 

400 

.      R400 

.      R.400 

.      R.400 

600 

1200 

IGO 

320 

.      R.800 

400 

.     R.400 

400 

600 

600" 

400 

.     R.400 

400 

600 


ClilNA. 


Pieces  {'■)' 
the  Ton. 
R.400- 
R.800 


X-ankeen  cloth 

Silks',  of  all  sorts     •• 

Chiiui  ware,  .30  cabical  feet  totlie  ton, 
or  about  4  cl.-ests  of  the  Uiual  di- 
mensions. 

Other  measurable  goods,  50  cubical 
feet  to  the  ton. 

N.  B.  Where  the  letter  R.  is  set 
asainsi  pieces  of  400  to  the  ton,  it 
shews  those  goods  nre  to  be  reduced, 
or  brought  to  a  standard  of  %6  yard* 
loiiiz  and  1  broad. 

Where  again.4  pieces  of  800  to  t]:c 
toil,  to  10  yards  long  and  I  broad. 

tXAMPI-F. 

1000  pieces  of  12  yards  long  and  1-J 
broad,  at  400  to  the  ton,  make  8 14 
pieces,  ©r  2  tons  44  pieces. 

1000  pieces  of  lOf  yards  long  and  1^ 
broad>  at  800  to  the  ton, "is  1181^ 
pieces,-  or  1  ton  381  pieces. 


WEIGHABLE  GOODS. 


A'rrangocs 

Aloes  •  • 

Benjamin    

Borax 

Cardemons,  fine  goods 

Gakelack    •  •  • 

Carraenia  Wool 

Cambogium    

Cassia  Lipnea- ....... 

Cassia  Buds    

Camphire 


Cut.  to 
the  Ton. 

'iO 

....    16 


20 
12 
16 
10 
20 
8 
12 
1.5 


Cotton  Yarn/  Fine  Goods  •..•••    10 } 
Cowries*  •••Gruff^di'to  • 
Coffee* •••••Pine  do.    • 

Cinnabar     

Gloves    ,  . .  .^. 

Dragon's  Blood 

Gum  Arabic    

•  ^^•Elerai ••  • 

» .^^ .  Amaiooiacuro 


T% 


20 
18 
10 
12 
20 
16 
16 
16 


CiCU   ^9 

the  Ton, 

Gum  Opoponax 1  (1 

•  •  •  •  Satjapenum     •    18 

. . .  •  Sarcocol  ....-•.•• 18^ 

Indigo    12 

Iron  Kintlage    20 

Musk .^  ..*..... 20 

Myrrh    1  <J 

Mother-of- Pearl  Shells 20 

Nux  Vomica 15 

Pepper 15 

Quicksilver     20 

Rhubarb ».•      » 

Raw  Silk 10 

Ditto  in  cheats     B 

Ditto  in  bales  or  bundles    lO 

Hetiwood    20^ 

Rice 20 

Shellack Id 

Serdlack     la 

Siicklack    •••••»•-•#  nti »•••-•  l# 


EXCHANCrK 


WEIGH  ABLE  GOODS 

Cut.  to 


?;a!t-Pelr 


the  Tor 


20 


Sago   •> 1^^ 

Pitto,  packed  ia  Ch^ia  ware  • '  •  •  — 

Tutenague <2{j 

TAirai'.ric       • j (t 

Xiucdl It) 


the  Ton. 

Tea,  Green - 8 

'  •  •  •  Bohea    10 

Arrack.  •  •  •  Gauge  gallons 251 

Canes Tale  oOO 

Wanghoes  and   Bar[ib(!es ■  3000 

Llattan^  equVl  to  16  cut. 6000 


ARBITRATION  o^  exchange: 

Whex  the  rates  of  exchanfrc  between  several  countries  m 
succession  are  given,  to  find  the  rate  ot  exchange  between  the 
^rst  and  last  phice  in  the  correspondence. 

Rule.  Find  by  proportion  (he  value  of  the  sum  originally 
remitted  in  the  different  monies  of  the  countries  through  which 
it  passes  according  to  tiie  rates  of  the  different  exchanges  and 
so  proceed  till  the  whole  is  finished.      Or, 

i\Iultiply  all  the  first  terms  of  the  difi'erent  statings  together 
for  a  divisor,  and  the  second  terms,  together  with  the  sum  re- 
mitted, for  a  dividend,  and  the  quotient  is  the  amount  received 
in  the  denomination  of  the  last  place  in  the  correspondence  : 
trom  this  result  the  rate  of  exchange  is  readily  found  by  pro- 
portion. 

Examples. 


1.  A  merchant  in  London  has  credit  for  500  piastres  in  Lcgi' 
horn  for  which  he  can  draw  directly  at  52d.  sterling  per  {)ias- 
tre;'but  chusing  to  have  it  remitted  by  a  circular  rout,  they  are 
sent,  by  his  orcljej,.  to  Venice  at  <)5  piastre*  for  100  ducats  ban- 
co ;  from  thence" to  Cadiz  at  350  maravedies  per  ducat  banco; 
from  thence  to  Li^bon  at  630  reas  per  piastre  of  ^72  marave- 
dies ;  from  thence  to  Amsterdam  at  48(/.  Flemish  for. 400  reas; 
from  thence  to  Paris  at  54-^/.  Flemish  per  crown  ;  ai^d  f"oni 
thence  to  London  at  30r/.  sterling  per  crown  :  Whiit  is  the  ar- 
bitrated price  between  London  and  Leghorn  per  piastre,  and 
>vhat  is  gained  or  lost  by  this  circular  rQuiiUunce  vnthout  reck*- 
^laing  cxpcnccs  ? 


AnBlTRATION  OF  EXCHANGE. 


525 


jtiaft. 

d.  ban. 

piast. 

d.  ban. 

9^ 

100 

:          500          : 

526^%  in  Venice. 

d.b. 

mor. 

fl.h. 

mar. 

1 

360 

::          520^ 

184210jf  in  Cadiz. 

mar. 

re</s. 

mcrr. 

rcas. 

272 

630 

::    1842lOl§ 

'.  426664      in  Lisbon. 

reus. 

d,jL 

rci/s. 

d.ji. 

400 

48 

::  426664 

51  \99l     in  Amsterdam, 

d.fl. 

cr. 

d.f. 

cr. 

54 

:           1 

::     511991 

:         94 S  ^6  in  Paris. 

cr. 

(L  St. 

( /'. 

£.     s.    d. 

1 

:       30 

::          9^-8  A 

118   10  44  sterling. 

Or  thus, 

piast.     d. 

b'.        mar. 

rraa.         r?.^. 

cr. 

95  X 

I   X  272 

X   400   X   54 

X   1=:55814400 

piust.      d. 

h.     mar. 

reus,     d  Ji.   cr. 

d.st 

500  X  100X350X630X48X  1  X  30zz  158760000000^ 

558144|00)15876OOO0OOl0O  )  28444^ 

III62S8  

2|0)237|0  4l 


4713120 
4465152 

24796'80 
2232576 

2471040 
2c:32576 

2384640 

2232576 

15206i 
4 


^.118   10  4i  as  abore. 


piasf.  £.     s,    (l.     piast.     d, 
500  :  118    10  44  ::  1   :   SmU 


>5SM4)60S.'56(4 
558144 


50112  £.  s.     d. 

Amount  received  l)y  circular  remittnnce     118  10  4^ 

500  piastres  at  52c/. • 108     6  8 

C  Gained  by  circular  remittance     •  •  •  •    ^.10     ^ 

C  Arbitrated  value  oJ  a  piastre  by  do. 


t^-i  ARBITRATION  OF  EXCHANGE.- 

2.  A  merchant  in  Boston  has  £.225  sterling  in  LonsJvm 
1^'hich  he  can  draw  for  at  5-^d,  sterling  per  dollar,  but  chusin^; 
to  try  a  circuhir  rout  it  is  sent  to  Dublin  at  .£.100  sterling  foi- 
i^.  109  Irish  ;  ihcnce  to  Hamburgh  at  12^  marks  banco  per 
pound  Irish  ;  thence  to  Amsterdam  at  33  florins  for  40  marks 
banco  ;  thence  to  Copenhag^en  at  5  florins  for  2  rix  dollars  of 
Denmark;  thence  to  Bremen  at  3  marks  per  rix  dollar  of  Den- 
mark ;  thence  to  Russia  at  5  marks  for  2  rubles  ;  thence  to 
Bordeaux  at  5  francs  per  ruble  ;  thence  to  Cadiz  at  18  reals 
plate  for  10  francs  ;  ihcnce  to  Lisbon  at  1250  reals  plate  for 
100  milreas  ;  thence  to  Leghorn  at  750  soldi  for  88  miircas  ; 
thence  to  Smyrna  at  2  soldi  per  piastre  ;  thence  to  Jamaica  aS 
24^7.  Jamaica  currency  p^r  piastre  ;  and  thence  to  Boston  at 
80r/.  Jamaica  currency  per  dollar  :  What  is  gained  or  lost  by 
this  circular  remittance  ?. 

Ans.  117  dols.  42  cts.  gained.. 


AMERICAN  DUTIES 

ARE  CALCULATED  AS  IN^  THE  FOLLOWING 

EXAMPLES. 

1.     What  is  the  duty  on  2885  gallons  of  molasses,  at  5  ctti*. 
per  gallon  ? 

2885 
5 


1-4425  cents.  Ans;  144  dols.  25  ct^,. 

1^  2.  What  is  the  duty  on  the  above  molasses,  if  imported  in  a- 
foreign  vessel,  the  rate  being  65  cents  per  gallon,  or  10  per 
cent,  more  than  an  American  vessel  ? 

2885  Or,  144,25  as  above. 

5.§  10  per  cent.        14,42. J 

14425  dol*.      }6S,67k 

1442i- 


4ol».  15  8^67  i 


An5.  158doi8.  67 J  c«t»;. 


AMERICAN  DUTIES.  2?5 

3.     How  much  is  the  duty  on  3720  gallons  of  gin,  at  31  ^^^ 
eents  per  gallon  ? 

3720  3720 

31 1^0  9 


3720      10)33480 

11160  

3348  3348 


dols.  1186',6*8  Ans.  1186  dols.  68  cent*. 


^                                              dols.  ctt» 

4.  1273  lb.  chocolate  at  3  cents  • Ans.  38  ly 

5.  Q65  lb.  do.  in  a  foreign  vessel  at  3,^o  do.  •  •  •  •  31  84 J 
6*.     1 149  lb.  cheese  at  7  ditto    •  •  • .  80  43 

7.  1295  lb.  do.  in  a  foreign  vessel  at7i^  do.  *  *  * '  99  T'l  J 

8.  1879  g<ils.  Champaign  wine  at45  do.  •••••  t  •  •845  55 

9.  2675  do.  London  particular  Madeira  at  5S  do. 1551  50 


10.     What  is  the  duty  on  53  cwl.  2  qrs.  21  lb.  of  untarred 
Cordage,  at  225  cents  per  cwt.  ? 
225 
53 


'*.,t. 


5  qrs. 
14  lb. 
7   do. 

I 

i 
-      h 

675 
1125 

28 
14 

Ans.  120  dols.  79^  ct». 

i 

120,791 

11.     What  is  the  duty  on  the    aboVe    cordage  in  a    foreigia 
vofc^cl,  at  247J  cts.  per  cwt.  ? 

Ans.  132  dok.  87^  cts* 


fte  AMERICAN  DUTIES. 

12.  How  much  is  the  duty  on  4  hhds.  of  brown  su^ar,  wt. 
gross  38  cwt.  3  qrs.  19  lb.  tare  12  lb.  per  100,  at  2h  cents  per 
lb.  ?  ^  ^ 

3800 
456'~exccss  12  per  cent, 
84 
19  ^ 

gross     4359  4359 

>ar^         52a  12  V 


3836  i23,0Ji 

^2- 


7672 
1918 

95,90 


Anr^.  0^  t^^la.  S'O  ^'tf. 


13.     What  is  the  duty  on  this  sugar,  in  a   foreign  vessel,  at. 
§f  cents  per  lb.  ? 

Ans,~10-5  dols.  49  cts. 


The  mode  of  eslimating  ad  valorem  rates  of  dufij. 

The  ad  valorem  rates  of  duty,  irpon  goods,  wares  and  mer- 
chandizes, at  the  place  of  importation,  shall  be  estimated  by 
adding  20  per  cent,  to  the  actual  cost  thereof,  if  imported  from 
the  Cape  of  Good  Hope,  or  from  any  other  place,  bryond  tlie 
same,  and  10  per  cent,  on  the  actual  cost  thiMcof,  if  imported 
from  any  other  place  or  country,  includir.g  all  charges,  com- 
misssions,  outside  packages  and  insurance  excepted^ — f6Vc  Laus^ 
of  the  United  States.) 


-^  AMERICAN  DUTIES.  227 

Examples. 

1.  What  is  the  duty  on  an  invoice  of  silver  and  plated  ware. 
Imported  from  London,  the  cost  exclusive  of  commissions,  &c, 
being  £,359  IS  4,  dt  15  per  cent,  ad  valorem  ? 

1^  359  ^    >         ^^  * 

444  cents  per  £.  sterling. 


143G 

14SG 

1436 

10^.       1 

222 

5      ■    ^ 

111 

3  4rd.i 

74 

actual  cost     139803  centi 
10  per  cent,  added   139SO 

175783 


10  ,\  1757S 

5  I  8789 

for  15  per  cent.         2636*7  cents. 

Ans.  263  dols.  €7  cents. 

2.  What  will  it   amount  to  in  a   foreign  vessel,  at  16J  per 
cent,  ad  valorem  ?  Ans.  290  dols.  4  cents. 


The  rates  at  'which  all  forrign  coins  and  currencies  are  estimate  j 
at  the  Custom- Houses  of  the  United  States, 

Dols.  Cts. 

Each  pound  sterling  of  Grent  Britain,  at    4     44 

Each  pound  sterling  of  Ireland    ••• 4      10 

Each  livre  touriiois  of  France • 18| 

Each  rlorin  or  gilder  oilhe  Unit<-d  Netherlands     ••  40 

Each  mark  hanco  of  J lamburgii . . •• 33 J 

Each  rix  dollar  of  Denmark     1 

Each  real  oi'  -late  of  Spain • 10 

Each  n-al  of  vcilon  of  Spain     » .  > 5 

Each  jiiilr-vie  of  Portugal 1     24 

Each  tale  of  China *^^^ ^      ^^ 

Each  pagoda  of  i ndi'a  •  •  ••d||y * i      S4 

Each  rupee  of  Bengal  •  •  .jJT.  • #••...  50 


(228  ) 

PR  OG  RE  SSION 

Consists  in  two  parts — Arithmetical  and  Geometrical. 


ARITHMETICAL  PROGRESSION' 

Is  when  a  rank  of  numbers  increase  or  decrease  regularly, 
by  the  continual  adding  or  subtracting  of  some  equal  number: 
As  1,  2,  3,  4,  5 J  6,  are  in  Arithmetical  Progression  by  the 
continual  increasing  or  adding  of  one,  and  11,  9,  7,  5,  3,  1, 
by  the  continual  decrease  or  subtraction  of  two. 

Note.  When  any  even  number  of  terms  differ  by  Arith- 
metical Progression,  the  sum  of  the  two  extremes  will  be  equal 
to  the  two  middle  numbers,  or  any  two  means  equally  distant 
from  the  extremes  :  As  2,  4,  6,  8,  10,  12,  where  6-f  8,  the 
two  middle  numbers,  are  zz  12  -f  2,  the  two  extremes, 
and  rz  10  +  4  the  two  means  rz  14. 

When  the  number  of  terms  are  odd,  the  double  of  the  middle 
term  will  be  equal  to  the  two  extremes,  or  of  any  two  means 
equally  distant  from  the  middle  term  :  As  1,  2,  3,  4,  5, 
where  the  double  of  3=5+  lrz2  +  4  =  6\ 

In  Arithmetical  Progression  five  things  aret®  be  observed,  viz, 

1.  The  first  term. 

2.  The  last  term. 

3.  The  number  of  terms. 

4.  Tke  equal  difference. 

5.  The  sum  of  all  the  terms. 

Any  three  of  which  being  given,  the  other  two  may  be  found. 


Thejirst,  second  and  third  terms  given  to  find  the  fifth. 
Rule.     Multiply  the  sum  of  the  two  extremes  by   half  the 
number  of  terms,  or  multiply  half  the  sum  of  the  two  extremes 
by  the  whole  number  of  terms,  the  product  is  the  total  of  all 
the  terms. 

Examples. 

1.     How  many  strokes  docs  the  hammer  of  a  clock  strike  ia 

12. hours? 

12-i-lr=i3  f/;cw  I3x6lr=78  Ans. 
2'.     A   man  buys  17  yards  of  cloth,  and  gave  for  the   first 
;^';ird.  2.y.  aiid  for  the  last  iO^.  what  did  the  17  yards  amount  to? 

Ads.  £%^  2s, 


rnOGRRSSION.  2<?<9 

3.  If  100  eggs  were  piaccd  in  a  riglit  line,  exr.ctly  n  3-nrd 
asunder  from  one  another,  and  the  first  a  yard  from  a  basket, 
what  length  of  ground  does  that  man  go  who  gathers  up  theJ^e 
100  eggs  singly,  returning  with  every  egg  to  the  basket  to  put 
it  in  ?  '  Ans.  5  riiilcs,  1300  yards. 


The  first,  second  and  Ihird  fcrr.is  ghen  to  find  ilie  foiivilu 

lluLE.  From  the  second  subtract  the  (irit,  the  remainder 
divided  by  the  third  less  one  gives  the  fourth, 

KXAMTLES. 

1.  A  man  had  "8  sons,  the  youngest  was  4  years  old.  and 
the  eldest  32,  tliey  increase  in  Arithmetical  Progression  :  v»liat 
wa^  the  common  dilference  of  their  ac:es  r  Ans.  4, 

32— 4r:2S  then  28-r8^1=:4  the  co:.-  0. 

C.     A  man   is  to  travel  from  Boston    to  ;l  (    iUiin  p.i.ce    in 
12  days,  and  to  go  but    3  miles  the  first  (]a3%  increasing  every- 
day by  an  equal  excess,  so  that  the  last  day's  jourr.ey  may   be 
58  miles  ;  what  is  the  daily  increase,  and  liow  many  miles  dis- 
tant is  that  place  from  Boston  ?     Ans.  5  miles  daily  iKcrca,e. 
Tlierefore  as  3  miles  is  the  first  day's  journey  ', 
3-f  :5zz   8  second  ditto. 
6-1-5  =  13  third  ditto,  &c. 
Ilie  whole  distance  is  360  miles. 


The.  first,  second  and  fourth  terms  ghcn  iofind  the  tlard. 

Rule.  From  tlie  second  subtract  the  first,  the  remainder 
divide  by  the  fourih,  and  to  the  quotient  add  1,  gives  the 
third. 

Ex  AM  ELKS. 

1.  A  person  travelling  into  the  ^untry.  wcrd  3  miles  the 
first  day,  and  increased  every  day  by  5  mih's,  till  at  last  he 
went  58  miles  in  one  day  ;  how  inany  days  did  he  travel  ? 

Ans.    12. 

.^8—3  —  55  then  55~-5~U  an<[  1 1 -j-  1  —  12  the  number  of 
days.  ^ 


.C30  TROGIVESSION. 

'2.  \  :r.an  being  p.skcd  how  many  sons  lie  had,  said  that  the 
jv:.>...,>  -^t  was  4  xears  old,  and  the  ekiest  32,  and  that  he  in- 
treated  one  in  his  iamily  every  4  years  3  how  many  had  he  ? 

Ans.  8. 


T/ie  sccmJ,  flurd  and  fourth  given  fofijid  the  first. 

Rule.  Multiply  the  fourth  by  the  third,  made  less  by  \, 
the  product  subtracted  from  the  second  gives  the  first. 

Examples. 

1.  A  man  in  10  days  went  from  Boston  to  a  certain  town 
in  tlie  country,  every  day's  journey  increasing  the  former  by  4, 
ar.d  the  last  day  he  went  was  4-6  miles  ;  what  was  the  first  ? 

Alls.  10  miles. 

4  X  10— 1  =3()  then  46— 36 rr  10,  the  first  da^-'s  journey. 

9,  A  man  takes  out  of  his  pocket  at  8  several  times,  so  many 
dilTerenc  numbers  of  shillings,  every  one  exceeding  the  former 
by  6,  the  last  46'  ;  what  was  the  first  ?  Ans.  4. 


The  second  y  third  and  fifth  given  to  find  the  first, 

T:tm  r.  IVivide  the  fifth  by  the  third,  and  from  the  quotient 
b  irthe  product  of  the  fourth,  multiplied  by  the  third 

]•>:  AMPLE. 

A  m:in  is  to  receive  f ..j6o  at  \2  several  payments,  each  to 
c:\ceed  ti:e  f(;rmer  by  £A-,  and  is  willing  to  bestow  the  first 
payment  on  any  one  that  can  tell  him  what  it  is  ;  what  will 
"that  person  have  for  his  pains  ?  Ans.  ^'.8. 

4x17-^ 

S60— r2--30  then  30 =zS,  the  first  paymei^^ 


The  first,  third  and  fourth  given  tofnd  the  second, 
Uvi  !•.      Subtract  the  huirth  from  the  product  of  the   third, 


PROGRESSION.  231 

Example. 
What  is  the  last  number  of  an  Arithmetical  Progression,  be- 
lining  at  6',  aucA  continuing  by  the  increase  of  8  to  '20  places? 

Ans.   1.3S. 


oQxS— Sr=15<2  then  1524-6iz:158,  the  last  number. 


GEOMETIUCJL  PROGRESSIOX 

Is  the  increasing  or  decreasing  of  any  rank  of  numl-cis  by 
some  common  ratio,  that  i^,  by  the  continual  multiplication  or 
division  of  some  ecjual  number  :  As  ^,  4,  8,  l6,  inc!\v>se  by  the 
multiplier  2,  and  Iv),  8,  4,  2,  decrease  by  the  divide  .•  .'. 

Note.  When  any  number  of  terms  is  continued  m  Geo- 
metrical Progression,  the  product  of  the  two  extremes*  will  be 
equal  to  any  two  means,  equally  distant  from  the  extremes  : 
As  2,  4,  8,  16,  32,  64,  where  04  X  2z=4  X32zr8  X  l6i:zl28. 

When  the  number  of  terms  are  odd,  the  middle  term  multi- 
plied into  itself  will  be  equal  to  the  two  extremes,  or  any  two 
means  equally  distant  from  the  mean:  As  2,  4,  8,  l6,  32,  where 
2X32=:4X  l6nSx8  — ()4. 

In  Geometrical  Progression  the  same  five  things  arc  to  be  ob- 
served as  in  Arithmetical,  viz. 

1.  The  first  term. 

2.  The  last  term. 

3.  The  number  of  terms. 

4.  The  equal  dilference  or  ratio. 
I                    5.     The  sum  of  all  the  terms. 

Note.  As  (lie.  last  term  .in  a  long  series  of  numbers,  is  very  tedious  to  C(>r»c 
at,  by  continual  multiplication  ;  therelbre,  for  the  readier  finding  it  out,  there 
is  a  series  of  numbers  made  use  of  in  Arithmetical  Proportion,  called  indices, 
beginning  with  an  unit,  whose  coramin  diifeience  is  one,  whatever  nriiuher  of 
indices  3'ou  make  use  of,  set  as  many  numbor.s  ^in  such  G;'oii'?tncal  IVopoi- 
tion  as  is  given  in  the  question^  under  them  : 

.     1,  2,  3,     4,     5,     6  indices. 

2,  4,  8,  16,  32,  64  numbers  in  Geometrical  Proportion. 

But  if  the  first  term  in  Geometrical  Proportion  be  different 
from  the  ratio,  the  indices  m^st  begin  with  a  cypher. 

^^0,  1,  2,  3,    4,    5,    6  indices. 

1,  2,  4,  8,  16,  32,  64  numbers  in  Geometrical  Proportion. 


53:2  PROGRESSION. 

V;iien  tlic  indices  begin  with  acypiier,  the  sum  of  the  indices 
made  choice  of  must   he   always  one  less  than  the  number  of 

ternis  aivcn  in  the  question,  for  1  in  the  indices  is  over  the  se- 
cuiiJ  tfrin,  a:i,l  2  over  the  third,  kc. 

Add  any  two  of  the  indices  toii;cther,  and  that  sum  will  agree 
with  the  product  of  tiuir  respective  terms. 

As  in  the  lirst  table  ot  indices  2-f-    5zz     7 
Geometrical  proportion  ....  4  X  32zz  1^8 

Then  in  the  secoiul  ^'^~   t.—   ^. 

4x  ]6iz  64 

In  any  Geometrical  Progression  proceeding  from  unity,  the 
ratio  L-eii.g  known,  to  find  any  remote  term,  without  producing 
all  ihe  iLtennediate  terms. 

Rule.  Find  what  figures  of  the  indices  added  together  would 
give  the  exponent  of  the  term  wanted,  thcii  multip'ly  the  num- 
bers standing  under  such  exponent  into  each  other,  and  it  will 
give  the  term  required. 

Koiz.  Wlicji  t!ic  exponeiit  1  blands  over  the  second  terra,  the  number  of 
€iponc:its  m\ii>t  be  1  le^s  than  the  number  of  termi. 

Examples. 

1.  A  man  agrees  for  12  peaches,  to  pay  only  the  price  of  the 
last,  reckoning  a  farthing  for  the  first,  a  half-penny  for  the  se- 
cond, <Scc.  doubling  the  price  to  the  last ;  what  must  he  give  for 
them  ? 

0,  1,  2,  3,     4,  exponents.  l6'zi4 

J,  2,  4,  8,  16',  number  of  terms. 


!?56*n8 


MHO 


4-j-4-|-3— 11,  number  of  terms  less!.  - 


4) 2048 iz  11  numb,  farlh. 
12)512 
20)42  8 


£.2  2  8  answer. 

2.  A  country  gentleman  goitjg  t6  a  fair  to  buy  some  oxen, 
metis  with  a  person  wdio  had  23,  he  demanding  the  price  of 
thcn^,  was  nnbwered  £.16'  a  piece;  the  gentleman  bids  him  £.15 


PROGRESSION.  233 

jipiecr,  and  be  woiiUl  buy  all;  the  other  tells  him  it  would  not 
be  taken,  but  if  he  would  give  what  the  last  ox  would  come  to, 
at  a  farthing  for  the  first,  and  doubling  it  to  the  last,  he  should- 
have  all.     What  was  tiie  price  of  the  oxen  ? 

Ans.  £Ao6g   Is,  Ad. 


In  any  Geometrical  Progression,  not  proceeding  from  ur^ity, 
the  ratio  being  given,  to  lind  any  remote  term,  without  pro- 
ducing all  the  intermediate  terms. 

Rule.  Proceed  as  in  the  last,  only  o])sorvc  that  every  pro- 
duct must  be  divided  by  the  first  term. 

Examples. 

1.  A  sum  of  money  is  to  be  divided  among  eight  persons,- 
the  first  to  have  .£.20,  liic  ^iecond  J^.60,  and  so  on  in  triple 
proportion,  what  will  the  last  have  ? 

540x510  I'tjSOxCO 

0.     1.       2.       3. — M5S0thcn =1:43740 

20.  60.  ISO.  510.        20  20 

Ans.  ^.437-10.^ 
3  +  3+IZ-7  one  less  than  the  number  of  terms. 

2.  A  gentleman,  dying,  left  9  sons,  to  whom  and  to  his  ex- 
fcutor,  he  bequeathed  his  estate  in  manner  folio wdng  :  To  his 
executor  ,£.50  ;  his  youngest  son  was  to  have  as  much  more  as 
the  executor,  anel  each  son  to  exceed  the  next  younger  by  as 
much  more  ;  wh:it  was  the  eldest  son's  portion  ? 

Ans.  £.2.36'00. 


The  first  term,  ratio,  and  number  of  terms  given,  to  find  tiic 
sum  of  all  the  terms. 

Rule.  Find  the  last  term  as  before,  then  subtract  tlie  first 
from  it,  and  divide  the  remainder  by  the  ratio  less  one,  to  the 
product  of  which  add  the  greater,  and  it  gives  the  sum  re- 
(juired. 

l\XA  ?.i  r  r.ES. 

1.  A  servant  skilled  in  numbers  agreed  with  a  gentleman  to 
serve  him  12  month*^,   provided   he  would  give  him  a  farthing 


1^34  PROGRESSION. 

for  liis  first  month's  service,  a  penny  for  the  second,  and  Ad,  for 
l!iC  ilurd,  t^s:c. — what  did  his  wages  amount  to  ? 

Q56  X  '256zz65536,  then 65536  X  64- 41£)430-i 

0.  1.     ?.     3.       4.  4154304—1 

1.  4.  1().  (5+.  ?5(). rz  1398 101;  then 

(4-f  4-f  Szzll.  No.oftermslessl.)        4—1 

1398101 -|-41f)4304=:z55f}C>405  farthings. 
Ans.  £.5SQ5   Ss,  5i(l. 

2.  A  man  bought  a  h.orse,  and  by  agreement  was  to  give  a 
far  tiling  for  the  iir>t  nsil,  three  lor  the  secon:],  t<c.  ;  tliere  v.erc 
4  shoes,  and  in  each^  shoe  S  nails  ;  what  was  ^hc  wt'rth  of  the 
lior^e  ?  Ans.  £.(j6'o  11 4681  ().93    13.9.  4c/. 

3.  A  certain  person  married  his  daughter  on  new-^-ear's 
('•av,  aiid  gave  hvv  liiisband  one  shilling  towards  her  portion, 
promising  to  doulde  it  on  the  lirst  day  of  every  month  for  one 
\ear;  wiiat  was  her  portion  ?  Ans.   £.Q0^   I5s, 

4.  A  L^iccmaii  vad!  versed  in  numbers,  agreed  witli  a  gen- 
t Ionian  to  sell  him  Q'-^  yards  of  rich  gold  brocaded  lace;  lor  2 
]  in^  the  first  yard,  ()  pins  the  swond,  <kc.  in  triple  proportion. 
i  (iesire  to  know  \\h:a  l.e  sold  tlie  lace  for,  if  the  pins  were  val- 
n(\d  iit  100  for  a  farthing  ;  also,  what  the  laceman  got  or  lost 
I'V  tlic  sale  thereof,  supposing  the  lace  stood  liiin  in  ^.7  per 
^a^d,  Ans.  The  lace  sold  for  £.326886  Os,  od. , 

Gain  £.326732  C.v.  (}c/; 


~  PFAlMUTAriON 

^>  the  chan^iniz  or  varying  of  the  order  of  things. 

"a 
V:  c].E.      Multiply  fil  the  given  terms  one  into  another,  and 

th.'  labi  |?roduct  will  be  the  number  of  changes  required. 

KXAMPLES. 

1.  IT  )w  many  clninges  may  be  rung  upon  12  bells,  and  how 
loni:  vvould  V\cy  be  ringing;  but  once  over, supposing  10  changes 
i.r:  :ht  L(^  rang  iri  oiie  minute,  and  the  year  to  contain  36o  days 
('  lioui-s  r 

1  X2x3X4xr)X6x7  XSX9X  10X11  X  12  =  479C*Ol6CO 
i^-;)g(^S    whirii  -^  10r=47900l60   minutes,  t\nd   it    reduced 


PER  MUTATION.  235 

2.  A  young  scholar  coming  into  a  town  for  the  conveniency 
of  a  good  library,  dcnmnds  of  a  gentleman  with  whom  he  lodg- 
ed, what  his  diet  would  cost  for  a  year,  who  told  him  ^*.10  ; 
hut  the  scholar,  not  being  certain  what  time  he  should  stay, 
asked  him  what  he  must  give  him  for  so  long  as  he  could  place 
his  famil)^  (consisting  of  6'  persons  besides  himself)  in  difi'erent 
positions,  every  day  at  dinner;  the  gentleman,  thinking  it  could 
not  be  long,  tells  him  £.5,  to  which  the  scholar  agrees  :  what 
lime  did  the  scholar  stay  with  the  gentleman  ? 

Ans.  5040  days^ 


EXTRACTION  ov  th^  SQUARE  ROOT: 

ExTRACTixG  THE  Square  Root  is  to  find  out  such  a 
numher  as  being  multiplied  into  itself,  the  product  will  be  equal 
to  the  given  number. 

PcULE.  1.  Point  the  given  number,  beginning  at  the  unit's 
j^lace,  then  to  the  hundred's,  and  so  upon  eveiy  second  figure 
throughout. 

2.  Seek  the  greatest  square  number  in  the  first  point,  to- 
wards the  left  hand,  placing  the  square  number  under  the  first 
j^oint,  and  the  root  thereof  in  the  quotient;  subtract  the  square 
number  from  t!ie  first  point,  and  to  the  remainder  bring  down 
the  next  point  and  call  that  the  resolvendf 

3.  D<|nble  the  quotient,  and  place  ItJ^c^S^drvisor  on  the 
left  hand  of  the  resoivend  ;  seek  how  often  the  divisor  is  con- 
tained in  the  resoivend  (reserving  always  the  unit's  place)  and 
put  the  answer  in  the  quotient,  and  also  on  the  right  hand  side 
(f  the  divisor  ;  then  multiply  by  the  figure  last  put  in  the  quo- 
tient, and  subtract  the  product  from  the  resoivend;  bringdown 
the  next  point  to  the  remainder  (if  there  be  any  more)  aixd 
proceed  as  before. 

Roots.       1.     f:.     3.     4.     5.     ().     7.     S.     .9. 
^bQUAUi^s.  1.     4.     :),   16\  25.  ^0'.  4f).  64.   SU 


* 


t3G    EXTRACTION  OF  THE  SQUARE  ROOT. 

Examples. 
1.  What  is  the  square  root  of  1 19025  ? 

119025(31-5 
9 

64)290 
25() 


685)34.25 

34:25  Ans.  S'^S. 


2;  What  is  the  square  root  of  10^929  ?  Ans.     327 

5.  What  is  the  square  root  of  22GS741  ?  Ans.  1506*,23-f 

4.  What  is  the  square  root  of  7596795'  ?  Ans.  2756,22S-{- 

5.  What  is  the  square  root  of  3t)3729()l  ?  Ans.  603i 
•  6.  Wlvdi  is  the  square  root  of  22071204.  ?  Ans.  46'93 

When  the  given  number  consists  of  a  whole  number  and  de- 
cimals togetuery  make  the  number  of  decimals  even,  by  adding 
cj^phers  to  tliem,  so  that  there  may  be  a  point  fall  on  the  unit's 
place  of  the  whole  number. 

7.  What  is  the  square  root  of  3271,4007  ?     Ans.  57,19H- 

8.  What  is  the  square  root  of  4795,25731  ?  Ans.  60,247  + 

9.  What  is  the  square  root  of  4,372594  ?        Ans.  2,091  -f 
10.  What  is  the  square  root  of  2,2710957  ?     Ans.  1,50701-f- 
H.  What  is  the  square  root  of  ,00032754  ?     Ans.  ,01809-f 
12.  Wi;at  is  the  square  root  of  1,270054  ?       Ans.  1,1209  + 

1,  

To  extract  iJ^  square  roof  of  a  "c  id  gar  fraction. 

Rule.  Reduce  the  fraction  to  its  lowest  term'^,  then  extract 
the  square  root  of  the  numerator  for  a  new  luimerator,  and  jhe 
square  root  of  tlie  d.onominator  for  a  new  (ieiK^minator. 

If  tlio  fraction  be  a  surd,  (i.  e,)  a  number  whose  root  can- 
ncvor  bo  exactly  found,  reduce  it  to  a  decimal,  and  extract  the 
root  from  it. 

Examples'. 

\3,  \Vhat  is  the  square  root  of  5.20  +.  }  /^.m.  |,- 

14.  What  is  the  square  root  of  vJH^  ?  Ans.  f. 

15.  What  i»  the  square  root  of  1^5'/'.  ?  Ans.   f'. 


EXTRACTION  OF  THE  SQUARE  ROOT.        ^Z7 

Surds* 

16\  What  is  the  square  root  of  V^  ?  Ans.  ,89802  + 

ir.  What  is  the  square  root  of  J  f  J  ?  Ans.  ,86'602  + 

18.  What  is  the  square  root  of  \\%}  Aus.  ,93-OS-f 


To  extract  the  square  root  of  a  mixed  nimiher. 

Rule.  1.  Reduce  the  fractional  part  of  the  mi.xed  number 
to  its  lowest  term,  and  then  the  mixed  number  to  an  improper 
fraction. 

'2.  Extract  the  roots  of  the  numerator  and  denominator  for 
a  new  numerator  and  denominator. 

If  the  mixed  number  gi\en  be  a  surd,  reduce  the  fractional 
part  to  a  decimal,  annex  it  to  the  whole  number,  and  extract 
the  square  root  therefrom. 

Examples. 

19.  WHiat  is  the  square  root  of  5l|{  ? 

20.  What  is  the  square  root  of  27/^6  ^ 
2L   What  is  the  square  root  of    9|^  ? 

Surds. 

22.  What  is  the  sciuare  root  of  S5lf  ? 

23.  What  is  the  square  root  of  8f  ? 
2-l!.   What  is  the  square  root  of  6'|  ? 

The  Application. 

1.  There  is  an  army  consisting  of  a  certain  number  of  men, 
who  are  placed  rank  and  iile,  that  is,  in  the  form  of  a  square, 
each  side  having  576  men,  I  desire  to  know  how  many  the 
whole  square  contains  ?  Ans.  331776. 

2.  A  certain  pavement  is  made  exactly  square,  each  side  of 
^vhich  contains  ^7  ^^^i^t,  I  demand  how  many  scpiare  feet  are 
contained  therein  ?  Ans.  9409. 


Ans. 

n- 

Ans. 

6-i. 

Aus. 

3f. 

An; 

5.  9.*: 

7-^- 

An: 

s.  2,9 

-'3i9-f 

An: 

<.  2,5 

^^98-1:- 

Tojlnd  a  mean  proportional  between  any  two  given  numbers. 

Rule.     The  square  root  of  the  product  of  the  given  num- 
bers is  the  mean  proportional  sought. 


238   EXTRACTION  OF  THE  SQUARE  ROOT, 

Examples. 
1,  What  is  the  mean  proportional  between  3  and  12  ? 
Ans.  3  X  12—36  then  v'SOzzO"  the  mean  proportional. 

5.  What  is  the  mean  proportional  between  427^  and  842  ? 

Ans.   1897,4  + 


Tofind  the  side  of  a  square  equal  in  area  to  any  given  super  feces. 

Rule.     The  square  root  of  the  content  of  any  given  super* 
ices,  is  the  square  equal  sought. 

Examples. 

-   3.     If  the  content  of  a  given  circle  be  \60,  ^vhat  is  the  side 
•f  the  square  equal  ?  Ans.   12,64911. 

4.     If  the  area  of  a  circle  is  7^0,  what  is   the  side  of  the 
square  equal  ?  Ans.  27,386 12. 


The  area  of  a  circle  given  to  find  the  diameter. 

Rule.  As355  :  452,or  asl  :  1,273230  ::  so  is  the  area  ;  to 
the  square  of  the  diameter  ; — or,  multiply  the  square  root  of 
the  area  by  1,12837,  and  ttic  product  will  be  the  diameter. 

Example. 

5.  What  length  of  cord  will  tit  to  tie  to  a  cow's  tail,  that 
other  end  iixed  in  the  ground,  to  let  her  have  liberty  of  eating 
nn  acre  of  grass,  and  no  more,  supposing  the  cow  an;!  tail  to  be 
5  yards  and  a  half?  Ans.  6,136  perches. 


T/ie  area  of  a  circle  given  to  find  the  periphery,  or  circumference. 

Rule.  As  113  :  1420,  or  as  1  :  12,56637  ::  the  area  :  to  the 
square  of  the  periphery,  or  multiply  the  square  root  of  the  area, 
by  3,3449,  and  the  product  is  the  circumference. 


SQUARE  ROOT. 


239 


Examples. 

6,  When  the  area  is  IQ,  what  is  the  circumference  ? 

Ans.   12,^798. 

7.  When  the  area  is  l60,  what  is  the  periphery  ? 

Ans.  44,84. 


Ani/  tivo  sides  of  a  rigid  angled  triangle  given  to  find  the  third 

side. 

1.     The  base  and  perpendicular  given  to  find  the  hypothec- 

lUlsC. 

Rule.  The  square  root  of  the  sum  of  the  squares  of  the 
Jjase  and.  perpendicular  is  the  length  of  the  hypothenusc. 

Examples. 

8.  The  top  of  a  castle  from  the  ground  is  45  yards  high^ 
ftnd  is  surrounded  with  a  ditch  6'0  yards  broad  ;  what  length 
muit  a  ladder  be  to  reach  from  the  outside  of  the  ditch  to  \\v^ 
top  of  the  castle  ?  Ans.  7.5  yards. 


if;    o 


Ditch. 


JZS 


Base  00  yards. 

p.  The  wall  of  a  town  is  2.5  feet  high,  which  is  surrounded 
by  a  moat  of  30  feet  in  breadth,  I  desire  to  know  the  length  of 
a  ladder  that  \^  ill  reach  from  the  outside  of  the  moat  to  the  top 
of  the  wall.  Ans.  3^,03  feet. 


The  hypofhenuse  and  perpendicidar  given  to  find  the  base. 

Rule.     The  square  root  of  the  difrerencc  of  the  pquares  of 
the  hypothenusc  and  perpendicular  is  the  length  of  th-  base. 


no  SQUARE  ROOT. 

The  base  and  /ivpofJtcnii.yc  giren  to  find  the  'perpendicular. 

Rule.  The  square  root  of  the  djffcreiu'e  of  the  hypothenus© 
and  base  is  the  height  of  the  perpendicuhir. 

N.  P).    The  two  last  qucslions  may  be  varied  lor  examples  to  (he  two  last 
pro])ositious. 


Any  number  of  men  being  given  to  form  them  into  a  square  bat'- 
tic,  or  to  find  the  number  of  ranks  and  files. 

Rule.  The  square  root  of  the  number  of  men  given,  is  the 
number  of  men  either  in  rank  or  file. 

10.  An  army  consisting  of  331 77()  men,  I  desire  to  knovV 
how  many  in  rank  and  file  ?  Ans.  bl6. 

11.  A  certain  square  pavement  contains  48  841  s(juare 
stones,  all  of  the  same  size,  I  demand  how  many  are  contained 
in  one  of  the  sides  ?  Ans.  221. 


EXTRACTION  OF  THE  CUBE  ROOT. 

To  extract  the  Cube  Root  is  to  find  out  a  number  v»hich  Ic- 
ing nuiltiplied  into  itself,  and  then  into  that  product,  produccth 
the  given  number. 

Rule  1.  Point  every  third  figure  of  the  cube  given,  begin- 
ning at  the  unit's  place,  seek  the  greatest  cu))e  to  the  fist  j^.oint 
and  subtract  it  therefrom,  ])ut  the  root  in  tlie  quotient,  and 
bring  down  the  figures  in  the  next  point  to  the  remainder  for  a 
resolvend. 

2.  Find  a  divisor  by  multiplying  the  square  of  the  ({uoticnt 
by  3.  See  how  often  it  is  contained  in  the  resolvend,  rejecting 
tliC  units  and  tens,  and  put  the  .answer  in  the  quotient. 

3.  To  find  the  subtrahend.  1.  Cnbe  the  Inst  figure  in  the 
q'jotient.  2.  INIultiply  all  the  figures  in  the  (juotient  by  3  ex- 
cept the  last,  andthatproductby  thescjuare  of  the  hist.  3.  INIul- 
tiply the  divisor  by  the  last  figure.  Add  t]u\-e  products  togeth- 
er, gives  the  subtrahend,  which  subtract  from  the  resolvend;  to 
the  remainder  bring  dov.m  the  next  point  and  proceed  as  before. 

Roots.     ].       2.       3.       4.       5.       C).       7.       S.       p. 
Cubes.    1.       8.      27.     64.     125.  Clu.  343.  512.  729. 


CUBE  ROOT.  ^^^ 


Example. 
What  is  the  cube  root  of  99252S47  ? 

99252847(463 
G4zzCube  of  4. 

Divisor. 

Squareof4x3zz4S)35252  Resolvend 


j^lGzzCube  of  G 
432    iz:4  X  3  X  by  square  of  6 
288      —Divisor  X  by  G 


33336  Subtrahend 

Divisor. 

Sq.  of  46  X  3=6348)  1916847  ResoKcnd 


27=Ciibc  of  3 
1242   zn^'S  Xo  A  b}'  square  of  3 
19044      ^Divibor  X  by  3 


1916847  Subtrahend. 


Anotlier  nexD  and  more  concise  method  of  extracihig  the  Cube 
Root. 

Rule.  1.  Point  every  third  figure  of  the  cube  given  be- 
ginning at  the  unit's  phice,  then  find  the  nearest  cube  to  the 
first  point,  and  subtract  it  therefrom,  put  the  root  in  the  quo- 
tient, bring  down  the. figures  in  the  next  point  to  the  remaind- 
er for  a  resolvend. 

2.  Square  the  quotient  and  triple  the  square  for  a  divisor — ■ 
as,  4X4X3:ii4S.  Find  how  often  it  is  contained  in  the  re- 
solvend, rejc^ctiiig  I' nits  and  tens,  and  put  the  answer  in  the 
quotient. 

3.  Square  I  he  his-t  figure  in  the  quotient,  and  put  it  en  the 
right  hand  of  the  divisor: 

As  6x6=^36  put  to  the  divisor  48  =r.  4836. 

4.  Triple  the  last  figure  in  the  quotient,  and  multiply  by 
the  former,  put  it  under  tiie  other,  units  under  the  teiis,  add 
them  together,  and  multiply  the  sum  by  the  last  figure  in  the 
quotient,  subtract  that  product  from  the  resolvend;  bring  down 
the  next  point  and  proceed  as  before, 

X 


'3  ^  CUBE  ROOT. 

Examples. 

\s\nit  is  the  cube  root  of  <}9252847  ?  / 

Square  of  4  x  3=48  divisor  59252847  (463 

Square  of  6  put  to  48=4836  ()4. 

O'X  3X411:   72  


35252 


5556'      X      6     =  33336 

Square  of  46=2116x3=6348  divisor . 

Square    of  3=9  put  to  6348=*634809  19l6S47 
3X3X46=          414 


6389^9  X  3=  1916847 


2.  What  is  the  cube  root  of  389017  ?  Ans.  73. 

3.  What  is  the  cube  root  of  5735339  ?  Ans.  179. 

4.  What  is  tlie  cube  root  of  32461759  ?  Ans.  319. 

5.  What  is  the  cube  root  of  8  V601519  ?  Ans,  439. 

6.  What  is  the  cube  root  of  259694072  ?  Ans.  638. 

7.  VVhat  is  the  cul^e  root  of  48228544  ?  Ans.  364. 

8.  What  is  the  cube  root  of  27054036008  ?  Ans.  3002. 

9.  V,  hat  is  the  cube  root  of  22069810125  ?  Ans.  2805. 

10.  What  is  the  cube  root  of  12261532/232  ?  Ans.  4968. 

11.  What  is  the  cube  root  of  2  19365327791  ?  Ans.  6031. 

12.  What  is  the  cube  root  of  673373097125  ?  Ans.  8765. 

Wbien  ,  irani])er  consists  of  a  whole  number  and  de- 

cimal toiv  ,  i.^ake  tb.e  number  of  decimals  to  consist  of  3, 
6,  9>  ^C'  ph:"('  .,  by  adein::  cypliers  thereto,  so  that  there  may- 
be a  point  fall  on  the  unit's  place  of  the  whole  number. 

13.  What  is  the  cube  root  of  12,977875  ?  Ans.  2,35 

14.  What  is  the  cube  root  of  361d5,0':7576  ?  Ans.  33,C6-f 

15.  What  is  the  cube  root  of  ,001906624  ?  Ans.  ,124 

16.  What  is  the  cube  root  of  33,2--0079637  ?  Ans.  3,2l5-f 

17.  What  is  the  cube  root  (  :  72504  ?  Ans.  25,l6-f 

18.  What  is  the  cube  root  01  /     _  .    /279  ?  Ans.  ,376  + 


*  When  1]^,  quotient  is  j,  2,  or  3,  there  m\i\\  Ic    a    (;yp],er  put  to  suppij" 
the  ])lace  of  tens. 


CUBE  ROOT.  24S 

To  extract  the  cube  root  of  a  'vulgar  fraction. 
Rule.  Reduce  the  fraction  to  its  lowest  terms,  then  extract 
the  cube  root  of  the  numerator  and  denominator  for  a  new  nu- 
merator and  denominator;  but  if  the  fraction  be  a  surd,  reduce 
it  to  a  decimal,  and  then  extract  the  root  from  it. 
Examples. 

19.  What  is  the  cube  root  of  gt|  ?  Ans.  |. 

20.  What  is  the  cube  root  of  {\\^q  ?  Ans.  I. 

21.  What  is  the  cube  root  of  l{l%  ?  Ans.  ■:. 

SuiiDS. 

22.  What  is  the  cube  root  of  t  ?  Ans.  ,829  + 

23.  What  is  the  cube  root  of  ^3  ?  Ans.  ,822  + 

24.  What  is  the  cube  root  of  §  ?  Ans.  ,873  + 


To  extract  the  cube  root  of  a  mixed  number. 

Rule,     Reduce  the  fractional  part  to  its  lowest  tenuis  ninl 
then  the  mixed  number  to  an  improper  fraction,    cy" 
cube  roots  of  the  numerator  and  denonuiiJitor  f.r  li  1 
rator  and  denominator  ;   but  if  the  nii:.  1    Ll  a 

surd,  reduce  t!ie  fractional  part  to  a   c;.^ —    ,  ,......:.  u   to  U.y 

wliijle  iiaUib'jr,  and  extract  the  root  therefrom. 


Examples. 

25.  What  is  the  cube  root  of  12^f  ?  Ans.   2\. 

9ii  What  is  the  cube  root  of  3lX^.5  ?  A;. 

27.  What  is  the  cube  root  of  405  i^Aj  ?  A... 

Surds. 

28.  What  is  the  cube  root  of  71  ?  Ans.   1,93  + 

29.  What  is  the  cube  root  of  9 J  ?  Ans.  2,002  + 
SO.  M'hat  is  the  cube  root  of  8f  .?                 Ans.  2,057  + 

The  Appltcatiois^. 

1.  If  a  cubical  pi-oce  of  timber  be  47  inclies  lon?^,  47  inches 
broad,  and  4:7  inches  deep,  how  many  cubical  inches  doth  it 
contain  ?  Ans.  103823. 

2.  There  is  a  cellar  dug  that  is  12  feet  every  way,  in  length, 
breadth,  and  depth,  how  many  solid  feet  of  eaitli  were  taken 
out  of  it  ?  Ans.  172s. 


^U  CUBE  ROOT. 

3.  ThcM'c  is  a  stone  of  a  cubic  form,  which  contains  3S9017 
solid  (cot;  what  is  the  supcriicial  content  ofone  of  its  sides  ? 

Ans.  5329. 


Bctxeen  fico  7iitmhcys  ghen,  to  find  tKo  mean  proporfio?2als. 

Rule.  Divide  the  greater  extreme  by  the  lesser,  and  the 
cube  root  of  the  quotient  multiplied  by  the  lesser  extreme  gives 
tlie  less'jr  mean;  multiply  the  said  cube  root  by  the  lesser  mean, 
and  th^  product  will  be  the  greater  mean  proportional. 

Examples. 

4.  What  are  the  two  mean  proportionals  between  6  and  1(}2? 

Ans.  18  and  54. 

5,  V\'hat  are  the  tvv^o  mean  proportionals  betv.cen  4  and  108? 

Ans.  \2  and  36. 


To  find  the  side  of  a  c  III  e  that  shall  he  equal  in   solidity  to    any 
gken  solid,  as  a  globe,  cylinder,  prism,  cone,  SfC, 

Rule.  The  cube  root  of  the  solid  content  of  any  solid  body- 
given  is  the  side  of  the  cube  of  equal  solidity. 

Example. 

6.  If  the  solid  content  of  a  globe  is   lOCiS,  what  is  the  side 
of  a  cube  of  equal  solidity  .?  Ans.  22. 


The  side  of  the  cube  being  given,  to  find  the  side  of  that  cube,  that 
shall  be  double,  treble,  ^^c.  in  quantity  to  the  given  cube. 

Rule.  Cube  the  side  given,  and  multiply  it  by  2,  3,  »Scc. 
the  cube  root  of  the  product  is  the  side  sought. 

Example. 

7.  There  is  a  cubical  vessel,  whose  side  is  12  inches,  and  it 
is  required  to  iind  the  side  of  another  vessel  that  is  to  contain 
liiree  times  as  much?  Ans.  17?30(}, 


BIQUADRATE  ROOT.  545 

EXTRACTION  OF  THE  BIQUADRATE  ROOT, 

To  extract  the  Inquaclrate  Root  is  to  ila,!  out  a  iuiiribci> 
\\hich  being  involve.!  IjW):  tii:;c.  i..  >  "  '.":  will  prcduco  the 
given  number. 

Rule.  First  extract  the  square  root  of  the  given  luimber, 
then  extract  the  squaic  root  of  that  squaie  root,  and  it  v.iil 
give  the  l/iquadrate  root  required. 

Examples. 

1.  What  is  the  biquadrate  of  27  ?  Ans.  53U4:K 

2.  What  is  the  biquadrate  of  76'  ?  3336"2176. 

3.  What  is  the  biquadrate  of  273  ?  57191-^0625. 

4-.  What  is  the  biquadrate  root  of  531441  ?  27. 

5.   What  is  the  biquadrate  root  of  33302176  ?  7(>. 

6".  What  is  the  biquadrate  root  of  57  1914-0625  ?  275. 


J  GENERAL  RULE 

rOR  EXTRACTING  THE  ROOTS  OF  ALL  POWERS. 

1.  Prepare  the  number  given  for  extraction,  b}^  pointing 
off  from  the  unit's  place,  as  the  root  rc(;iiiic.l  direct:-;. 

2.  Find  the  first  tipure  in  the  root,  by  liie  table  of  pov.er^, 
\vhich  subtract  from  the  given  number. 

3.  Brin<:  down  the  first  fv-iwvQ  'u\  \\\q  r::.t  point  to  tlie  re- 
mainder, and  call  it  ihe  dividend. 

4.  Involve  the  root  into  tlie  next  inferior  [lower  to  that  \vi;ich 
is  given;  multiply  it  by  the  given  power,  and  call  it  the  divisor. 

5.  Find  a  quotient  figure  by  common  division,  and  annex  it 
to  the  root  ;  then  involve  the  whole  root  into  the  given  power, 
and  call  that  the  subtrahend. 

.  (k  Subtract  that  number  from  as  many  points  of  tjc  given 
power  as  is  brought  down,  beginning  at  the  lowest  place,  and 
to  the  remainder  bring  down  the  first  figure  of  the  next  point 
for  a  new  dividen-l. 

7.   Find  a  new  divi ->:()!•,  and  proceed  in  all  repect-  a.^  before. 

X  2 


i>4^'  RULE  FOR  EXTRACTING,  &c. 

Examples. 
1.     What  is  the  square  root  of  14137^  ? 


141376(376 
9 

G')d1  dividead  oX-ziG     divisor    . 

37Xo7— 1369  subtrahend 

1369  subtrahend  37X^^r=:74     divisor 

376  X376zz  141376  subtrahend 


74)     447  dividend 


141376  subtrahend  Ans.  376. 

2.  What  is  the  cube  root  of  53157376  ? 

53157376(376 

27 

S7)261  dividend  oXoxS—^7  divisor 

37X^7X37— 50653  subfraliend 

50653  subtrahend  37X^'37x3i=:4107  divisor 

S76y,37 6y(,S7 6zi:ooi57 37 6  subtrahend 

4107)25043  dividend 

53157376  subtrahend  Ans.  37^ 


S..  What  is  the  biquadrate  root  of  1998717337(5  I 


199871733?6(376 
81 


108)1188  dividend 


1371161  subtrahend 


e026U')  1245.363  dividend 

19987173576  subtrahend- 


3   X    "    X    •'^   X    4  zzlOS  divisor 
''7X   -''"X   '>*'X   37iz;18?416l  subtraliciid 
:>7X    '^^X    ^^7X    4  =202612  divisur 
5-.?6X376X376X376— 15987173376  subtrahend 

Ans.  376.. 


DUODECIMALS,  ?47 

DUODECIMALS. 

Duo  DECIMALS,  OF  Cross  Multiplication,  is  a  rule  made  use 
of  in  measuring  and  computing  the  dimensions  of  the  several 
parts  of  buildings  ;  it  is  likewise  used  to  find  ships*  tonnage  and 
the  contents  of  t)ales,  cases,  &c. 

Dimensions  are  taken  in  feet,  inches,  and  parts. 

Artificers*  work  is  computed  by  different  measures,  viz. 
Glazing,  and  masons*  fiat  work,  by  the  foot  ; 
Painting,  paving,  plastering,  &;c.  by  the  yard. 
Partitioning,  flooring,  roofing,  tiling,  &c.  by  the  square  of  100  (t^ 
Brick-work,  &c.  by  the  rod  of  iG^j  feet,  whose  square  is  2/25. 

The  contents  of  bales,  cases,  &c.  by  the  ton  of  40  cubic  feet. 
The  tonnage  of  ships,  by  the  ton  of  ^S  feet. 


rult:  for  multiplying  duodecimally^. 

1.  Under  the  multiplicand  write  the  corresponding  denom- 
inations of  the  multiplier. 

2.  Multij^ly  each  terrain  the  multiplicand,  (beginning  at  the 
lowest)  by  the  feet  in  the  multiplier  ;  write  eacli  result  under 
each  respective  term,  observing  to  carry  an  unit  from  each 
lower  denomiiuition  to  its  superior. 

3.  In  the  same  manner,  multiply  the  multiplicand  by  the 
inches  in  the  multiplier,  and  write  the  result  of  each  term,  one 
place  more  to  the  right  hand  of  them,  in  the  multiplicand. 

4.  V/ork  in  the  same  manner  with  the  other  parts  in  the 
multiplier,  setting  the  result  of  each  term  two  places  to  the 
right  hand  of  those  in  the  multiplicand,  and  so  on  lor  thirds, 
fourths,  <^c. 

o.  Pi-occcd  in  the  like  manner  v>'ith  all  tlie  rest  of  tlie  dc 
nominatiuii^.  and  their  sum  will  give  the  answer  required*. 


U$  DUODECIMALS. 

Examples. 
1.     Multiply  4  feet  9  inches  by  8  inches. 

V    8 


Ans.  3  (eet  2  inches. 


Multiply  9  feet  6  inches  by  4  feet  9  inches. 

^  9        6 
4        9 

/?.  ?«.  

9  6x4   feetzzSS         0 

9  6x9  inc.3:  7         1-6 


45         1  6 

Ans.  45  feet  1  inch  and  6  twelfths. 

3.  Wliat  is  the  price  of  a  marble  slab,  whose  length  is  5  ket 
7  inches,  and  breadth  1  foot  10  inches,  at  1  dolhir  per  foot  ? 

Ans.  lOdols.  23  cents. 

4.  There  is  a  house  with  three  tiers  of  windows,  3  in  a  tier, 
tiie  height  of  the  first  tier  is  7  feet  10  inches,  of  tlie  second  6 
feet  8  inches,  and  of  the  third  5  feet  4  inches,  and  the  breadth 
of  each  is  3  feet  11  inches  ;  what  will  the  gliizin:;^  corae  to,  at 
14^/.  per  tbot  ?  Ans.  £.13    lis.   lOUL 

5.  If  a  house  mea<^ures  within  the  walls  52  feci  8  inches  in 
lengtli,  and  30  feet  6"  inches  in  breadth,  and-^tlie  roof  be  oi' a 
true  pitch  or  tlie  rafters  J  of  the  breadth  of  the  building,  what 
will  it  come  to  roDliugat  10^.  6d,  per  square  ? 

Ans.  £.12   12^.  ni. 


DUODECIMALS.  249 

Application  of  Duodecimals. 

To  find  how  many  cubic  or  solid  square  feet  (in  order  to  ascer^ 
tain  the  freight)  are  contained  in  cases,  baleSj  4^c.  that  is,  hoi» 
tnani/  cubic  feet  they  uill  take  up  in  a  ship. 

Examples. 

1.    Suppose  the  dimensions  of  a  bale- to  be  7  feet  6  inches,  3 
feet  3  inches,  and  1  foot  10  inches  ;  what  is  the  solid  content? 
ft.      in. 
7         6 
3         3 
ft'  in. 


7"  6X3  ft.=:^'2         6 
7  6X3  m.—  1       10 


2'1         4 
1        10 


i\.  in.  tw. 
21     4     6X1  ft.zz24         4         6 
24     4     exiOin.— ^0         3         9 


44         8         3 

Ans.  44  feet  8  inches  and  3  twelfth  parts. 

2.  What  is  the  freight  of  a  bale  containing  65  feet  9  inches^ 
at  15  dollars  per  ton  of  4-0  feet  ? 

tlccinially. 
65,7  b 
1.5 

S'28r5 
6575 


(Joh.  cts. 

1 5,00  for  40  feet 

20  ft. 

i 

7,50 

5  ft. 

I 

4" 

1,87,5 

6  in. 

1 

1  0 

,18,7 

3 

i 

,09,3 

40)986,'25 


24,65,5  24,65,6 

Ans.  24  dols.  65\  cts. 

3.  A  merchant  imports  from  London  6  bales  of  the  follow- 
ing dimensions,  viz. 

Length.               Ileiglit,  Depth. 

ft.     in.                ft.     in.  ft.     in. 

No.   1.              2     10              2     4  19 

2.  2      10              2     6  13 

3.  3        6              2     2  18 

4.  2      10              2      8  19 

5.  2      10              2     6  19 

6.  2     U              2     8  13 


25d  DUODECIMALS. 

What  are  the  solid  contents,   and  how  much  will  the  freight 
amount  to,  at  20  dollars  per  ton  ? 
""  Feet. 

71,58 

20dols.pcrton« 


The  contents  arc,  viz. 

ft.    in. 

No.  1. 

11     7 

2. 

8  10 

3. 

12     7 

4- 

13     2 

b. 

12     5 

6. 

13     0 

71     7 


40)1431,60 

o5,79 
Ans.  35  dols.  79  ctf» 


To  find  SJti/s  Tonnage  hj  Carpentcr^s  Measure. 

Rule.  For  single  decked  vessels,  multiply  the  lengthy 
breadth  at  the  main  beam,  and  depth  of  the  hold  together,  and 
divide  the  product  by  95. 

Example. 

What  is  the  tonnage  of  a  single  decked  vessel,  whose  length 
is  60  feet,  breadth  20  feet,  and  depth  8  feet  ? 
60  length 
20  breadth 

1200 

8  depth 


95)9600(1019^5 

100 
95 

5  Ans.  101/^  tons. 

Iliis  is  tlie  usual  method  of  tonnaging  a  single-decked  vessel,  liaving  tlie 
deck  bolted  to  the  wale.  13ut  if  it  be  required  that  the  deck  be  bolted  at  any 
lieight  above  the  wale,  the  custom  is  to  pay  the  carpenter  for  okg  half  of  the 
additiooal  height,  to  which- the  deck  may  be  thus  raised  ;  tliat  is,  one  half  of 
the  difference  bein^  added  to  the  former  depth  givoo  the  depth  to  be  used  ia 
calculating  the  tomiage. 


DUODECIMALS.  251 

Example. 
A  merchant,  after   having  contracted  with  a  carpenter   to 
t>uild  a  single-decked  vessel  of  6'0  ieet  keel,  20  feet  beam,  and 
8  feet  hold,  desires  that  the  deck  be  laid  for  10  feet  hold  ',  re- 
quired the  tonnage  to  be  paid  for  ? 

6'0  length 
20  breadth 

1200 
1=J  diff.  of  depth +  S  zz  9 

95) 10800(1 13ff 
95 

130 
95 

3.50 
65  Ans.  Ii3t)f  tons. 


Rule.  For  a  double-decked  vessel,  take  half  the  breadth 
of  the  main  beam  for  the  depth  of  the  hold,  and  work  as  for  a" 
single  decketl  vessel. 

Examples. 
1.     What  is    the  tonnage  of  a    double-docked  vessel,  whose 
length  is  6'j  lect,  and  breadth  21  feet  6  inches  ? 

65       length 
i?l  6  breadth 


65  ft.  X 6  in. r: 


in. 


ft  

1397  6xl0rt.rrl39r5  0 
1397  6x   9  in-=T  1043  1 


95)15023  1(43895- 

475 

"773 
760 


1^  Ans.  ioSll  tons, 


25f!.  DUODECIMALS. 


The  preceding  question  may  be  wrought  thus 

65 
21  6 

65 

130 

6 

i      1365 

32  6 

6 
3 

■  1397  6 
10  9 

13975  0 
i       69s  9 

i      349  4 

95)15023    1  as  before. 

15SJ5  tons. 

2.     What  will  the  above  tonnage  amount  to,  at  I6  dols.  per 
ton  ? 

dols. 
158  16 

16  13 

948  48 

158  16 

2,18  

95)208(2,18 

2530,18  190 


180 

850 
76'0 

Ans.  2530  dols.  IS  cents.  90 

3.   Required  the  tonntigc  of  a  ship  of  74  fcc-t   keel,  and   26 
feet  6  inches  beam  ?  Ans.  273 gy  tons. 


DUODECIMALS.  555 

To  find  the  GoTcrrnnent  Tonnage, 
*' If  tlic  vessel   be    double- decked,    take    the   Icivo/Ji    tliereof 
from  the  fore  part  of  the  main   stem,  to  ;    the 

stern  post,  above  the  upper  deck  ;  the  1;   :    i!,.  .    :   ..L-.the 

broadest  part  ^bove  the  main  wales,  half  of  which  ])rca(lth  shall 
be  accounted  the  depth  of  such  vesrel,  and  then  deduct  from 
the  length,  three-fifths  of  the  breadth,  multiply  the  re'ir.-iiiuler 
by  the  breadth,  and  the  product  by  the  depth,  and  divide  tliis 
last  product  by  95>  ^1^^  quotient  wiiereof  shall  be  deemed  the 
true  contents  or  tonnage  of  such  ship  or  vessel  ;  and  if  such 
ship  or  vessel  be  single-decked,  take  the  length  and  breadth,  as 
above  directed,  deduct  from  the  said  length  three-fifths  of  the 
breadth,  and  take  the  depth  from  the  under  side  of  the  deck 
plank,  to  the  ceiling  in  the  h©ld,  then  multiply  and  divide  as 
aforesaid,  and  the  quotient  shall  be  deemed  the  tonnage." 
Examples. 
1.  What  is  the  government  tonnage  of  a  single-decked  vessel, 
whose  length  is  69  feet  6  inches,  breadth  22  feet  6  inches,  and 
depth  8  feet  6  inches  ?  ft.  in. 

69  ()  length,         22  6  breadth 
deduct  13  G  for  |  breadth.   3 


56'  0  5)67  6 

22  6  breadth.    

13  6' 


112  0 

112 
6  in.      i  28  "0 


1260  0 

8  G  deptk 


10080  0 
G  in.      J        630  0 


9o}l0710  0(112j^  tons. 
321 


260 

iS)0 
70  _  Ans.  1121?  tens. 


25  4.  DUODECIMALS, 

^.  Wluit  is  the  government  tonnage  of  a  double-decked  rcs- 
sel,  oithe  following  dimensions;  length  75  feet  6  inches,  breadtk 
2o  feet  4  inches,  and  depth  3 1  feet  8  inches  ? 

75  6  ft. in. 

14  0  for  4  breadth  Or,  75  6 

14  0 

61  6 
23  4 


61  ^ 

23  4  breadth 

183 

122 

6  in. 

i 

11  6 

4  in. 

i 

20  6 

1435  0 

1 1   8  depth 

15785  0 

6  in. 

J 

717  6 

2  in. 

A. 

239  2 

61ft, 

X 

SSft.; 

—1403 

0 

6  in. 

X' 

L\'>ft.: 

zz     11 

6 

61ft.6in 

x 

4  ill. 

•r=    20 

6 

1435 

0 

11 

8 

15785 

1435  ft.  X  8 

m.r 

:     956 

8 

16741  8asb«forc 


95)16741   8(l70|i  tons. 
95 

724 
665 

591  • 

570 

21  Ans.  17611  tons. 

3.  What  is  the  government  tonnage  of  a  double-decked  ves- 
sel, of  the  following  dimensions ;  length  82  kei  3  inches,  breadth 
24  feet  3  inches,  and  depth  12  feet  Ih  inches  ? 

Ans.  209| f  tons. 


TABLES  OF  CORDAGE. 


255 


TABLES  OF  CORDAGE. 

A  Cordage  Table,  shewing  how  many  fathoms^  fed,  and 
inches  of  a  rope,  of  any  size,  not  more  than  14  inches,  male  a 
hundred  weight  ;  with  the  use  of  the  teible. 


i 

■  i    ^ 

p^  ^  >C 

Fathoms. 

Feet. 

Inches. 

•^ 

3     .  2 

i~ 

406  0  0 

4J: 

t'6  0  3 

7f 

~8~;Tr 

T(;y" 

'""■l'"f  o 

\\ 

313  3  0 

4| 

24  0  0 

8  3  6 

11 

4  0  3 

\\ 

216  3  0 

H 

21  3  0 

8 

7   3  6 

11^ 

3  5  7 

i| 

l^'O  3  0 

5 

19  3  0 

81 

7   -.   " 

' ' ' 

3  4  1 

« 

l'i4  V*)  0 

6| 

17  4  0 

U 

t; 

3  3  3 

51 

96  S  0 

51- 

1h    1    0 

8j 

(> 

3  'J  3 

77  3  0 

9 

65  4  0 

(j 

91- 

.» 

3 

54  0  0 

<3.l 

12   2  0 

p! 

5   ■:  o 

^  -  !-" 

'2  ?-  G 

'V- 

45  5  '2 

61 

11   3  0 

C;l 

5  0  6 

2  5  3 

.:jf 

39  3  0  j  Ql 

10  4  0 

vf 

4  5  0 

1.')^ 

2   1  9 

^ 

34  3  9  1  7 

9  5  6 

10} 

4  4   1 

1      ^• 

2    1  0 

4 

30  1   6 

7-- 

9   16 

lOi 

4  2  e 

1^ 

2  3  6 
2   2    1 

USE  OF  THE  TABLE. 

At  the  top  of  the  table,  marked  incites,  fathoms,  fvcf,  fnche?^, 
the  (irst  column  is  tlie  thickness  of  the  rope  in  inches  and  quar- 
ters, and  the  other  three  the  falfioms,  feet,  and  inches  that  make 
up  a  hundred  weight  of  such  a  rope.  One  example  will  make 
it  phiin  : 

Suppose  you  dA?sire  to  know  how  much  of  a  seven-inch  i'  o 
will  make  a  hundred  weight  :  Tiiul  7  in  the  third  column  un- 
der inches,  or  thickness  ol  rope,  and  against  it  in  the  fourth  col- 
umn you  find  9  5  6,  which  shews  that  there  will  be  9  fathoms 
5  ieet  6  inches  recj^uired  to  iiiake  one  hundred  weight. 


256 

A  T. 


TAELKS  OF  CORDAGE. 

■Jag  t'ic  urig/it  of  any  Cable  or  Rope  of  ICO  fuilj- 
,  ..:;ujur  Licri/  halj  inch,  from  5  to  'Z\  inc/us  hi 


i    -~ 

1   ^-   . 

i  ie 

Inches. 

G  6* 

t 

^  -i 

!  ;- 

0  '^* 

"^ 
s 

Cq^ 

3 

\i  i 

7 

12    1 

11 

30  i 

15^ 

&.)   0 

20 

100  0 

H 

S   0 

n- 

14  0 

11' 

S3  0 

16 

(M  0 

2()I 

105  0 

4 

4  0 

8 

Ui  0 

1-2 

oG   0 

16^- 

63  0 

21 

110  1 

1  41 

fj  0 

H 

18  0 

1^1 

39  0 

17 

72  1 

2U 

115  £i 

5 

6   1 

9 

20  1 

13 

42  1 

17^- 

76  2 

22 

121  Gl 

-^^ 

7  2 

9i 

22  '2 

131 

45  2 

18 

81  0 

c;oi 

1-26  2 

1  6 

9  0 

10 

'2b   0 

14 

49  0 

18i 

85  2 

23 

132  1 

0} 

10  2 

lOi 

27  i2 

14X 

52  2 

19 

90  1 

231 

138  0 

15 

56  1 

191 

95  0 

24 

141  0 

USE  OF  THE  TABLE. 

The  first  coiumn  marked  for  inches,  is  the  thickness  or  cir- 
cuniicrence  of  the  cable  to  every  half  inch  from  3  to  24  inch- 
es;  tho  bccoii.!,  rriarked  cwt.  qr.-.  for  the  hundred  weights 
and  quarters  that  it  \\\A  Wvi:;i],  it"  1*^0  fiUhoms  in  length. 

For  in-tance  :  Su;-,;jsc  it  be  a  cable  of  14^  inches  ;  look 
ligainst  14^  and  you  wiil  find  in  the  other  column  52cvvt.  2 
qrs.  which  shews  that  120  fathoms  of  14j  inch  cable  wall 
Aveigh  52cwt.  2qrs.  and  so  in  others :  and  any  quantity  of  a  less 
length  will  weigh  in  proportion. 

A  ship  was  brought  to  anchor  in  a  gale  of  wind,  but  the  gale 
increasing,  it  was  thought  safest  to  cut  the  cables,  in  conse- 
quence of  which  75  fathoms  of  l6  inches,  and  50  fathoms  of  12 
inches  were  lost;  what  must  they  be  valued  at  in  calculating 
the  average ;  new^  cordage  being  then  14  dollars  per  cwt  ? 

CALCULUrOX 

120f:il]i.  16in.  cable— 64  cv.t.  120  fatli.  12  in.cab.=:i36c\vt. 


60 do.... 

15 do  .. . 


•32 
.    8 


40 .do... 

10 do... 


...12 


75  fath.  weighing 
50 do.... 


50  luth.  weighing  • .  15 


.  40 

.15  — 

dols^  cts. 

55 cwt.  at  I4  dols.  pcrcwt..»«»770  00 
OhC  third  deducted  lor  new.  • .  •2")6     GS"] 


Answer— :Zcjij.  513     33 J 


TABLES  OF  GOLD  COIN. 


A 

TABLE 

^For  receiving 

and  }>ai/in<r 

Hie  'Gold Coins  of  France  and  Spain,  at 

100  cents  fur  '2]  3  grains  according  to  Act 

oJ  Congress, 

137  ths 

1 

37ths 

loTths 

grains 

dol.  cts.  oj 

''a  ct. 

chct. 

dfll  cts.  oJ 

^'  act. 

ounces.      dol.  cts.  oJ  a  ct. 

1    . 

.    0     3 

89 

J  2    . 

.      10   51 

13 

27 

.  •   472  .99     3/ 

2    . 

•  0     7 

41 

13    . 

.      11   38 

94 

28 

. .    490  51      13 

3    . 

.    0   10 

130 

14    . 

.      12   26 

3S 

29 

..50s      2    126 

4    . 

.    0    14 

82 

15    . 

.      13    13 

119 

30 

. .    525   54    102 

5    . 

.    0   IS 

34 

16   . 

.      14      1 

63 

31 

.  .    543     6     7S 

6   . 

.    0  21 

123 

17    . 

.      14   85) 

7 

32 

. .    560  58     54 

7   . 

.    0  25 

75 

18    . 

.      15  76 

88 

33 

.  .    57s    10     30 

8    . 

•  0  29 

27 

19    • 

.      16  60 

32 

34 

. .   595  62       6 

.9   • 

•    0  32 

116 

20    . 

.      17   51 

113 

35 

. .   613   13   119 

10   . 

.  0  36 

6s 

ounces 

36 

•.    630  65     95 

11   . 

.    0  40 

20 

1    . 

.      17  51 

113 

37- 

. .   61s    17     7i 

12  . 

•    0  43 

109 

2    . 

.      35     3 

S>9 

3S 

.   665  6i)     4  7 

13    . 

•  0  47 

61 

3    . 

.      52   55 

65 

S9 

-    683  21      23 

14    . 

.    0  51 

13 

4    . 

.     70     7 

41 

40 

•   700  72   136 

15    . 

.    0  54 

102 

5    . 

•     ^7  59 

17 

41 

-    718   24    112 

16    . 

•    0  58 

54 

6  . 

.    105    10 

130 

42 

•   735  76     St) 

17    . 

.  0  62 

6 

7   • 

.    122  62 

106 

43 

•    753  28     64 

18    . 

.  0  65 

9o 

8    . 

•    140    14 

82 

44 

.    770  80     40 

19    • 

•  0  69 

47 

9  • 

.    157   66 

58 

45 

.    7S8   32      16 

20    . 

.    0  72 

136* 

10   . 

.    175   18 

34 

46 

-    805   83   120 

21    . 

.   0  76 

88 

11  . 

.    192  70 

10 

47 

.    823  35    105 

22    . 

•    0  80 

40 

12  . 

.    210  21 

123 

48 

.    840  87      81 

23    . 

.    0  83 

129 

13  . 

.    227  73 

99 

49 

.    858  39     57 

24   . 

.    0  87 

81 

14   . 

.    245   25 

75 

50    . 

.    875  91      33 

dut. 

15    . 

.    262  77 

51 

51    • 

.    893  4'3       9 

1.    . 

.    0  87 

81 

16    . 

.    280  29 

27 

52    . 

•   910  9^   122 

2    . 

•    1  75 

25 

17    • 

•    297   81 

3 

53    . 

.   928  46     f}8 

3    . 

.   2  6*2 

106 

18    . 

.    315  32 

116 

54    . 

.  9-^5  98     74 

4    . 

•   3  50 

50 

19    • 

.    332   84 

9*2 

55    . 

.    963   50     50 

5    . 

•   4  37 

131 

20    . 

•    350  36 

68 

56   . 

.    9S1      2      26 

6  . 

•    5   25 

75 

21    . 

.   36'7  88 

44 

57    ' 

.   5A9S  54        2 

7  •. 

•   6  13 

19 

22    • 

.    385   40 

20 

58    . 

.1016     5    115 

8    . 

•  7     0 

100 

23    • 

.    402  91 

131 

59    • 

.1033   57     91 

9   • 

•  7  SS 

44 

24    - 

.    420  43 

109 

60    . 

.1051  .  9     67 

10  . 

•   8  75' 

125 

'25    . 

•    437  95 

85 

61    . 

.1068  61      43 

11    . 

•  9  63 

69^ 

26    . 

.    455  47 
Y2- 

61 

62    . 

.1086  13     19 

t53 


TABLES  OF  GOLD  COIN. 


A    TA BLE 

Tor 

rccching  andp 

ayiug  the  Gold  Coin 

^'o/'Great-Britain  andVor- 

tu 

gal,  r/^  lOOcT/i/^i^or^ 

7  grains  J  accordb 

(g  to  Act  oj  Congress. 

277/:5. 

( 

^ihs 

9th3 

^vs. 

dol.cts.  of  act. 

dwt. 

dol  ct^.  of  a  ct. 

OZ. 

(Jol.  cts.  of  a  ct. 

1 

••  0  3  19 

12  • 

•  10  66 

6 

28 

•  497  77     7 

«2 

'•  0  7  ]1 

13  • 

.   11  55 

5 

'2d 

•  •  515  55     5 

3 

'•  0  11  3 

14  . 

.   12  44 

4 

30 

-  533  33     3 

4 

'.  0  14  22 

\5    . 

•   13  S3 

3 

31 

.  551  11   1 

5 

..  0  18  14 

l6  . 

•   14  22 

o 

32 

.-  568  88   8 

6 

-  0  22  G 

17  • 

•   15  11 

1 

33 

.  586  66     6 

7 

•  0  25  2.5 

18  . 

.  i6  00 

0 

34 

.  604  44  4 

8 

•  0  29  17 

L9  • 

.   16  88 

8 

35 

.  622  22  2 

9 

•  0  33  9 

20  . 

•  17  17 

7 

36 

.  640  00  0 

10 

•  0  37  1 

ouncts 

37 

•  657  77     7 

11 

•  0  40  20 

1  . 

•  17  77 

7 

38 

.  675   55  5 

12  . 

•  0  44  12 

o     , 

.  35  55 

5 

39  • 

.  693  33     3 

IJ  . 

•  0  48  4 

3  . 

.  53   33 

3 

40 

.  711  11   1 

U 

•  0  51  53 

4  . 

.  71  11 

1 

41 

.  728  88  8 

15 

.  0  55  15 

5    . 

.   88  88 

8 

42 

.  746  66     6 

\G 

•  0  59  7 

6  . 

.  106  66 

6 

43 

.  764  44.  4 

17 

.  0  62  26 

7  • 

.  I'-n   44 

4 

44 

-  782  22  2 

18 

..  0  66  IS 

8  . 

.  142  22 

2 

45 

.  800  GO  0 

19 

..  0  70  iO 

9  • 

.  160  00 

0 

46 

-  817  77     7 

*20 

.  0  74  2 

10  . 

.  177  77 

7 

47 

•  835  55     5 

'21 

..  0  17   21 

11  . 

.  }()5  55 

5 

48 

.  853  33  3 

:-2 

.  0  81  \3 

12  . 

.  213  33 

3 

49 

•  871  11  1 

'  ', 

. .  0  85  5 

13  . 

.  231  11 

.1 

50 

.  888  88   8 

.  .  0  88  24 

jj,  . 

.  248  88 

8 

51 

.  906  66     6 

9ihs 

15    . 

.  266  66 

6 

52 

.  924  44  4 

*ii  t. 

UiJ.rtS.  9i\icl. 

16  . 

.  284  4i 

4 

53 

. .  942  22  2 

1 

.  .  0  88   8 

17  • 

.  302  22 

2 

5\ 

.  96'0  00  0 

o 

..  1  17     7 

18  . 

.  320  00 

0 

55 

.  977  77    7 

3 

. .  2  66    6 

19  • 

.  S'-J  77 

7 

56 

.  995  55     5 

4 

. .  3  55  5 

20  . 

.  355   55 

5 

57 

.1013  33     3 

5 

.  .  4  44  4 

21  . 

.  573  33 

3 

5% 

.1031  11   1 

() 

•  •  5  33  3 

22  • 

'    391  11 

1 

'^9 

.1048  88   8 

7 

.  .  6  22   2 

■4 -J      • 

.  408  88 

8 

60 

. 1066  66     6 

8 

..7  11   1 

21.  . 

.  426  66 

6 

6\ 

.1084  44  4 

9 

. .  8  00   0 

25  . 

.  4-44  44 

4 

62 

. 1  102  22  2 

10 

.  .  8  88   8 

26  . 

.  462  22 

9 

63 

.1120  00  0 

ii 

-  9  77  7 

27  • 

.  480  00 

0 

64  . 

.1137  77     7 

(  539  ) 

MERCANTILE  PRECEDENTS; 


BILL  OF  EXCHANGE. 

Neubiin/port,  Feb.  12,  1804. 

EXCHANGE  for  £.1000  sterling.. 

At  twenty  clays  sight  of  this  uiy  first  of  exchange  (second 
and  third  of  the  same  tenor  and  date  not  paid)  pay  to  John. 
Parker,  or  order,  One  Thousand  Pounds  Sterling,  with  ox 
without  further  advice  from 

Your  humble  servant,. 

WILLIAM  PRINCE. 
Messrs.  Dutton  &  Green, 
Merchants, 
LoDdon. 


BILL  OF  GOODS,, 

At  an  advance  on  the  sterling  cos^, 

Boston,  May  5,  ISO-K 
Mr.  William  Poole,. 

Bovg/i t  of  Elmo's  Si m m o n  d s , 

32  ells  mode Is.   8fA  sterl. £.2   13     4 

6*4  yds.  striped    Nankins    Is.  6d.  • '  » • 4    l6'     0 

28    .  •    striped  calico  1 6-.   C}.-/. • 2     9     0 

4  pieces  russel   •••...    24  y.  • . . .    4   i6     0 


SterL    14    14     4 
Exchange  33 J  per  cent.     4   18      l| 


£A9   12     5i 

Advance  at  20  per  cent.     3   18     53 

^^.23   10    II 


Dollars  78,48 
Fveceivcd  his  note  at  2  months, 

St 


2^0  MERCANTILE  PRECEDENTS. 

FROMISSORY  NOTE. 

Boston,  May  5.  1S04.  For  value  received,  I  premise  to  pav 
to  Simon  Sirniiionds,  or  order,  seventy-,  iglit  dollais  forty-eight 
cents  on  demand,  with  interebt  after  tv/o  months. 

Attest,  William  Poole. 

Saul  James. 


A  RECEIPT  FOR  JN  ENDORSEMENT  ON  A  NOTE. 

Boston,  July  12,  1804.  Received  from  Mr.  William  Poole, 
(by  the  hands  of  Mr.  Benjamin  I^iintO  1  hii  ty-eight  dollars 
seventy  cents,  which  is  endorsed  on  '        -te  of  May  5,    1804. 

ciMON  Simmon Ds. 
38  dols.  70  cts. 


RECEIPT  FOR  MONEY  RECEIVED  ON  ACCOUNT. 

Boston,  January  10,  1804.  Received  from  i\Ir.  D.  Evans^ 
(by  the  hands  ot  Mr.  Thomas  Dunmore,)  Four  hundred  and 
flirty  dollars  on  account. 

430  dols.  G-EORGE  Pace. 


PROMISSORY  NOTE  BY  TWO  PERSONS, 

Kevvluiryport,  l'2tli  July,  1804.  For  value  received  we 
jointly  and  sevenilJy  promise  to  pay  to  Mr.  Samuel  Rich,  or 
order.  Five  hundred  dollars  lifry-four  cents,  on  demand  Wftli- 
interest. 

Attest,  Nathan  Sayeotix. 

William  Bolton,  Stephen  Needy. 


GENERAL  RECEIPT. 

New- Bedford,  March  27,  1804.     Received  from  V.v.  N.  B. 
ten  dollars  Uventy-nine  cents  in  full  of  all  dcnmnds. 

10  dols.  29  cts.  E.  D. 


MERCANTILE  PRECEDENTS.  26l 

BILL  OF  PARCELS. 

A\':d'un/portj  June  20,  1S04). 
Mv.  William  IIolman 

Bought  o/' Daniel  Greei^", 
8  lib  lis.  sugar,  \\t.  viz, 

C.   q.      Ih.  C.   (f.    Ih. 

No.   1.  5  2  7  5.  b  3  UJ 

2.  5    1  22  6\  ^   1  17 

3.  6"  0  13  7.  5   1  7 

4.  5  2  13  8.  5   3  U 

22  2  27  22   2      i 

22  2      I 

45    1     0 
Tare  12percwt.  4311 

~ —  dais,   cti* 

Neat  40  1   17  at  12  duls.  per  c\vt,  ...•*.  484  83 

3  ijbls.  sugar,  v/r, 

C.  q.     lb. 

2  2  25 
1  3  17 

4  2   14 
Tare  21lb.  per  bbl.        1    14 

Neat     4   1     0  at  10  dels. 42  50 

3  hhds.  molabscs,  viz. 

gals. 

101—9* 

lOS— 5 

107—7 

316—21 
21 

295  gallons  at  50  cents 147   50 

1  quarter  cask  Malaga  wine 25   00 

5  cases  gin,  at  4  dois.  25  cts.    21    25 

Dols.  721   07 
*l'he  ullage  is  thus  uoted. 


^62  MERCANTILE  PRECEDENTS. 

INVOICES. 

INVOICE   of  20  hhds.  clayed  sugar  and    10  lihds.  coflfbe, 
shipped  by  .••...  of  Boston,  in  the  United  States  of  America, 

on  his  own  account  and  risqae,    on    board  the  ship , 

A.  B.  master,  bound  for and   a  market,  consigned  to 

the  said  A.  B.  for  sales  and  returns,  viz,    ■ 

50  hhds.  clayed  sugar,  viz. 


B.C. 

C.  q.  lb. 

C.  q.  lb. 

^0.  1  a  20 

Ko.  1.* 

11  3  14 

11. 

12  0   14 

2. 

. 10  3  21 

12. 

10  2   14 

3. 

110     0 

13. 

10  2  21 

4. 

12   1     0 

14. 

11  3  21 

5. 

11   1    14 

15. 

10  1   14 

0. 

10  3     7 

v;. 

10  2     0 

7. 

10  '2     0 

17. 

It  2  21 

8. 

11  0     7 

18. 

10  1  14 

9. 

11  0  ^1 

liJ. 

^J   1     7 

le. 

10  0     7 

20. 

10  a  u 

111  0 
110  2 

7 
0 

110  2    a 


Tare  12  per  cwt. 


197  3     8  neat, 

at  lOdoIs.  25cts. 

(loh.  rt,h 
2027   67 

30  hhds 

.  coffee,  wt.  viz. 

B.C. 

No.     C.  7.  /^.         r^re. 

No. 

C.  (/.  Ih. 

Tare. 

No.  1  a  : 

10       1.       9  2     7         108 

6. 

6  1   14 

79 

2.       9  3     0         112 

7. 

6  16 

61 

3.     10  1  21         106 

8. 

8  2     4 

84 

4.     10  2  14         103 

9. 

9   1     8 

91 

5.       8  0  14           94 

10.' 

10  0  14 

103 

48  2     0         5'23 

40  2    18 

42;* 

40  2  18         423 

946 

89  0  18  — 99861b. 

deduct  tare         946 

90401b.  neat  at  §1  cts.  1898  40 


3926  07 
Premium  of  insuring  4176  dols.  67  cts.  at  6  percent.     "^       ^^.^  ^^ 
to  corer  the  amouut' •••♦•••  ••- ....•     )      *' 

Bo}«..    4176  ^7 
Bo  tom^  fl-c. 


MERCANTILE  PRECEDENTS. 
INVOICE. 


2G3 


INVOICE  of  merchandize  on  board  the  brig  Swan,  A.  B. 
master,  shipped  by  A.  M.  on  his  own  account  and  risque,  for 
the  West  Indies,  and  consigned  to  said  master  for  sales  aiid  rer 
turns,  viz. 

140  M.of  boards  and  pbnk,  dol.  lOdols.  1400 

20  M.  of  white-oak  hhd.  staves30  6^00 

12M.  of  red'oak  hhd.     do.     12  144 

130  M.  shingles 3  390 

B.  No.  1—18.  1 8  hhds.  of  cod-fish,  173031b.    4pr.C.  692  12 

B.  No.  1— 52.   52  bbls.  of  beef 12  624 

E.  No.  1—30.  30  bbls.  of  salmon 10  300 

F.  No.   1 2.      2  bbls.  pork 18  SG 

L.  No.  1 7,      7  casks  of  rice,  neat  S9  C. 

3  qrs.  21  lb. 4pr.cwt.159  7B 

3  M.  of  hoops 25  75 

1300  pair  of  shoes  •  •  • 50  cts.  650 

Dols.   5070  8f 
Portsmouth,  Sept.  7,  1804. 

Errors  excepted, 

A,  M. 


Mr.  Abraham  Jones  to  Waller  Brown 


Br. 


1804. 

Jan.     5. 

8. 

p. 


Feb. 

IMar. 

May 


7. 

15. 

'29. 
5. 


For  1 
4 
9 
7 
3 
o 

5 

2 


barrel  of  flour Dols 

lb.  coffee •  •  •  2s, 

lb.  of  sugar 1  IrZ. 

gallons  of  molasses  •  •  •  •    os,  9d. 

quintalsoffish 15^. 

lb.  hysmi  tea 8.S.  Gd. 

lb.  chocolate 1^.  Gd. 

bushels  of  corn  ••....     4^.  9d. 


EiTors  excepted. 


10 
1 
1 

4 

7 

o 

1 
1 


33 
37 
2>7 
50 
S3 
25 
5S 


Dols.     30  23 


$(J4  MERCANTILE  PRECEDENTS. 

ACCOUNTS  OF  SALES. 
SALES  of^O  hhds,  7  htls.  and  31  hogs  coffee,  for  and  on  risk  of 

Mr,  William  Slillman,  wenhant  in  Portland, 

1804.  — —  .       ^ 

Marcli  15     William  Edcs,  ^0  hhds.  wt.       7       ^  ,     ^^^^     ^ 

14376  lb.  at  23  cts.  per  lb.  |      ^'^''  ^^^^  ^^ 

IG     George  Watts,  7  bbls.  wt.  1493at23  cts.    343  SQ 

17      Petci^ Bates,  31  bags,  5507      23         1266*61 

Charges,  4916  48 

Advertising*  • Dol.  1   46 

Storage • 3  50 

^  Commission  on .491 6  dols.  48  cts.  at  2  J 

per  cent.    122  pi  127  87 

Neat  proceeds  passed  to  his  credit    Do/5.478S  6I 
Errors  excepted,  &c. 

SALES  of  sundry  merchandize  received  per  the  ship  Juno,    Capt.    Dane,    from 
Machins  and  disposed  of  for  account  and  risk  of  Amos  Goodivin,  merchant  there. 


Date, 

To  whom  sold 

c 

-i5 

1 

i5 

tCii 

11 

C 
0 

1 

0 

X5 

Price 

a 

< 

1804. 

dis.cts. 

dols.cts. 

June  4 

James  Yates 

^0 

3 

90 

8 

Wm.  Howe 

120 

3  27 

292  40 

27 

John  Payson 

6 

12 

72 

July    4 

James   Nugent 
Cash 

.50 

^22 

4 

8  7.5 

88 

437   50 

8 

Sim.  Sands 

S,'^\6 

6  5 

20  90 

21 

Stock 

15 

9 

1:35 

29 

Paul  SImson 

Vo 

3  50 

45  50 

Aug.  6 

Jona.  Rose 
Taken  to  fiil  up 

1 

1,259 

6 

7  55 

1501  7 

.50 

1     1 13^22 

4,476 

15 

11' 88  85 

Jlemaining  unsold,  40  barrels  of  herring. 
Charges,  viz. 

-Storage  of  nsh • DoJs.    10  50 

Commission  on  1288  dols.  85  cts.  at  2J  per  cent.  32  22 

]S'eat  proceeds  carried  to  the  credit  of  his  acQOUiit, 
Errors  excepted,  &:c» 


42  7% 


Vols.  1246  13 


MERCANTILE  PRECEDENTS. 


565 


SALES  of  l^  hogsheads  and  7  barrels  of  rum,  received  per  the 
schooner  l\ul>i/,  Richard  Butler,  master  from  Fortsi/touth,  for 
account  and  risk  of  Daniel  Edwards,  7ner chant  thcre» 


5 

a 

Date. 

To  whom  sold. 

-a 

^ 

Contents. 

Amount. 

0 

P-i 

1804.    1 

Cts. 

dols.    cts. 

Maj24iBy  Walter  King 

1 

291 

io6 

29  50 

June   f  By  David  Jonss 

2 

ne 

100 

110  and  106 

216 

20;  [5y  Jarne*  Ray 

4 

438 

96 

108,110,111,109 

420  48 

24;  Jiy Aaron  Judson 

3 

81 

95 

26l,27|  27 

76  95 

July  23.ByTljo's  Ropes 

1 

115 

951 

109  82 

Aug.  s'ByParsonsicElv 

1 

25 

951 

23  87 

25 

By  3imon  Sands 

2 

222 

98 

109  113 

^]7  56 

Sept.  4 

By  Miles  Youna 

1 

1 

138 

96 

110     28 

132  48 

10 

By  Moses  Bliss 

.^ 

1 

342f 

99 

107,104,103,281 

339     7 

J^jByAiiiosDundas 

6 

— . 

65^ 

981 

109,162,106  > 
111,112,  92  5 

622  52 

19 

7] 

2239 

2183  2.J 


Charges. 

dls.  ets.  dls.  cts. 

Paid  Capt.  Butler  freight  of  19  hlids.  rum,  at    2  50  47  50 

ditto      ....  7  bbls. 66  4  62 

Porterage  19  hhds. •     40  7  60 

ditto        7bb!s.    ••         10  70 

Gauging    26  caiks 12|  3  25 

Cooperage  3  dols.  on  hhds.  1  dol.  50  cts.  on  bbls.  4  .50 

Advertiiing   •  • .  — 1   25 

Coaumisaioii  on  2io8  dols.  25  cts.  at  5  per  cent.  109  41 


178  83 


Neat  proceeds  • .  Dols.  2009  42 


Outstanding  in  hands  of 

dh.  cts. 

>([oses  BHss •..339     7 

Amos  Dundas  ...>.»  622  52 

Boston,  25th  Sept^mhcr,  1804. 

Errors  excepted,  5cc. 


Q66  mercantile  PRECEDENTS. 

y  nXS  of  the  Ship  Hi  raw's  Cargo,  hi/  WiUiam  Stiff  on. 

'  ^-  lb-         lio.  Hv.     sol.  den.  lie.  sol.  deti' 

..;,  Jl.G^y  ]\]\d.(i^-:,wt.  nt.  7^^537at33  per  100,  23953  14     2 

6  do.  (Jo. 6515     3-2 2084  16     0 

2  r\o.  do. oiS6     31 662     3     2 

.'^.4  do.  d). 36658     30 10997     8     0 

2  do.  parii^  d:im.-2184soidatauctiuuror     22'6     0     0 

— , 37924     1     4> 

109 

Vr.     sol.  den. 

24  !yh]s.  beef,  at  JOl      1    ,3perbbl.         2425  10     0 
7  do.     do. 99     8*5   695  18  11 

29  do.     do. 90  15     0 2631    15     0 

4  do.     do. 83     0     0   332     0     0 

6085     3  11 

64 

Ih.  sol. 
13  bbls.  pork 136  0 1768     0     0 

25  do.  porter   • 80  0 20(!0     0     0 

5  box.  liii.  con.  169  pice.     96  0  pr.  piec.  16224     0     0 
1]   i:ik.bulter,wt.ll^^9lb,     2  5  pr.  lb.     2540     5     0 

5  tl^ousandhoops 240       pr.  M.     1200     0     0 

59     do.      sbingles   16         do.  944     0     0 

15949  feet  boards 120         do.         1913  17     7 

170  sliakeu  hhds. 3}     pr.hhd.   1402   10     0 

27992  12  .7 

liv.     sol.   den.  7  2001   17  10 

Commission  on  7  2001  17  10  at  5  per  cent.  •  •  •  •      3600     1  10 

Liv.     68401   16     0 
Errors  Excepted,  &c. 

.1  )i^;hiir.s(-}f>ri.^fs,  D/fU/s,  Sc.  ]y'id  on  Ship  liiraw^  ffji  IVm.  Sutton, 

IS'.^'k  liv.     s.      d.     liv.     s.     d, 

i\i  ■<iy  1 8.   Fi)  id    for  a  barrel  of  flour 86  10     0 

(o  the  admiralty 240  1 1     6 

•  •  •  •    for  fresh  meat 56'  1 2     5 

fortiats  to   unload  uilh 341   13     6 

725     7     5 

Paid    to  the  harbour  master 66   10     4 

(  )i-ti»rrme  and  ne-ro  hav    619   14     8 

*'"    iur  inward  duties 714   11      7 

•  •  •  •    J'or  outward  duties    229   13     5 

1630   10     0 

]\tid    for  brokcra<ffe    '    821    13     6 

«••  '  •    for  passport  and  certificate 68   19     7 

890  13     1 

TobiUPctrc.  Guadabupc,  Jvb.j  12,  1804.  

J. IV.     3246  10     Q 
i^rroi.s  E.xccpkd,  ^c, 

wm.  sunoN. 


MERCANTILE  PRECEDEI^^TS. 


cc 


o 


p^--^  ^s 


^ 


'<2 


cc 


.»^ 


00   C^  CO 


cy 
o" 


:  2<:  c?  CO 

:    *^  rj^  rjH 

^  :  : 

'   00  Ai^  ^ 

'T*  iO  GO 


5  o    o 

5    ^  L-^   C* 

:   C/  r-i 

O 


CO 


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(     271     )  "* 

BILL  OF  SALE. 

TO  all  people  to  vvliom  this  present  Bill  of  Sale  shall  come,  I  R,  P.  of 
Kewburyporl,  in  tlic  Slate  of  JM;issachusetts,  Merchant,  send  Greeting  ; 
KNOW  YE,  That  I  the  said  R.  P.  for  and  in  consideration  of  the  sum  of 
three  thousandy  two  hundred  and  twriity-two  dollars,  to  me  in  hand  well  and 
Irnl^'  paid  at  or  before  the  ensealing  and  delivery  of  these  presents,  bj  S.  T. 
oi  the  said  Newburyport,  Merchant,  the  receipt  whereof  I  do  hereby  ac- 
knowledge and  am  there  with  fully  and  entirely  satisfied  and  contented,  have 
granted,  burgained  and  sold,  and  by  these  presents  do  grant,  bargain  and  sell, 
unto  the  said  S.  T.  all  the  hull  or  body  of  the  good  brig  Sally,  together  witU 
all  and  singular  her  masts,  spars,  sails,  rigging,  cables,  anchors,  boats  and  ap- 
purteaances,  now  lying  at  Newburyport,  and  registered  at  the  port  of  New- 
buryport, the  certificate  of  whose  registry  is  as  follows  : 

IN  pursuance  of  an  Act  of  the  Congress  of  the  United  States  of  America,  en- 
titled, **  A  i.  ACT  concerning  the  registering  and  recording  of  ships  or  vessels," 
11.  P.  of  Newburyport,  in  the  State  of  Massachusetts,  Merchant,  having  taken 
or  suhscrihed  tha  oath  required  hi/  the  said  act,  and  havii.g  sworn  that  he  is  the 
onlij  owner  of  the  ship  or  vessel  called  the  Sully,  of  Neichuryporl,  whereof  Wit- 
ii'tm  Smith  is  at  present  master,  and  is  a  citizen  of' the  United  States,  as  he 
hath  sworn,  and  that  the  said  ship  or  vessel  ivas  built  at  Salisbury,  in  the  said 
state,  in  the  year  seventeen  hundred  and  ninety-nine,  as  also  appears  by  a  certi- 
ficate of  enrolment,  No.  129,  issued  in  this  district  on  the  fourth  day  of  August 
last,  now  surrendered — and  N.  S.  Surveyor  of  this  district,  having  certified  that 
the  said  sltip  or  vessel  has  one  deck  and  two  masts,  and  that  her  length  is  slxtii- 
iiine  feet  five  inche'?,  her  breadth  twenty  two  feet  and  one  half  inch,  her  depth 
eight  feet  two  inches,  and  that  she  measures  one  hundred  and  six  tons  and  forty 
ninetyfifths,  that  she  is  a  square  sterned  brig,  has  no  galleries  and  no  figure 
head,  and  the  said  R.  P.  having  agreed  to  the  description  and  admeasurement 
above  specified,  and  sufficient  secu)  ity  having  been  given  according  to  the  said 
act,  the  said  brig  has  been  duly  registered  at  the  port  of  Newburyport. 

Given  under  my  hand  and  seal  at  the  port  of  Newburyport,  this  first  day  of 
January,  in  the  year  one  thousand  eight  hundred. 

To  have  and  to  hold  the  said  granted  and  bargained  brig  Sally  and  prem- 
ises with  the  appurtenances,  unto  the  said  S.  T.  his  heirs,  executors,  adminis- 
trators or  assigns,  to  his  only  proper  use,  benefit  and  behoof  forever.  And  T 
the  said  R.  P.  do  avouch  myself  to  be  the  true  and  lawful  owner  of  the  said 
brigand  appurtenances,  and  have  in  myself  full  power,  good  right  and  lawful 
anthorily  to  dispose  of  the  said  brig  as  aforesaid,  and  licr  appurtenances  in 
manner  as  aforesaid,  and  furthermore,  I  the  said  R.  P.  do  hereby  covenant 
and  agree  to  warrant  and  defend  the  said  brig  and  premises,  with  the  «ppur- 
tenances  against  the  lawful  claims  and  demands  of  all  persons  whaisoever  un- 
to the  said  S.  T.  In  witness  whereuf,  I  the  said  R.  P.  have  hereunto  set  my 
band  and  j^eal,  ihii  tcnlh  day  of  June,  iu  the  year  of  our  Loid  one  tboiuand 
cii-ht  hundred 


D; 


MERCANTILE  PRECEDENTS. 


]\I)\  Thomas  Gibson  in  interest 


dols,  cis. 

(laijs. 

(loLcfs, 

To  Int 

on  35  00  fr.  Jan.  31, 

'9Cr  to  Oct.  12/96,  256 

1  47 

To  do. 

on  2962   19  ..Feb.  2 

...to.. do.  ......  254 

123  68 

To  do. 

on  2500  42  .-May  31 

•  .<to..do. 131 

57  06 

To  do. 

on  1733  97  ..July  2- 

•••to.. do. 102 

29  07 

To  do. 

on  7o  63  .  'July  12  • 

...to '.do. 92 

1  u 

To  do. 

on  455  52  .  •  Aug. 25- 

• .  » to.  .do.  » 47 

3  51 

To  do. 

on  153  71  •  .Sep.  30 

...to.  .do. 12 

dols. 

0  31 

216  21 

Br. 


Mr.  fVilliam  Mace  in  interest 


20. 


1798. 
INI  arch 
April 
Au-.  18.. 
Dec.  28.. 
•99.Ja.  15.. 
Feb.  19.' 
March  20\  • 


dols.  cts,       y. 
To  Interest  on  386'9  20  for  1 


on    273    6 
-  on     400 
'  on    414     6 
'  on     200 
.  on    300 

on  1300 


7Jf.  d,              dols^  cfs, 
5  11 335  97- 

3  IS ..     21  29 

11  20 23  73 

7  10' 15  59 

79 7  SO 

5  25 8  75 

4  18 . .     29  90 

dols.     442  53 


MERCANTILE  PRECEDENTS.  275 


Account  with  Thomas  Merchant  Ci\ 

dols.  ct.                                    •               clays,  dols.ct. 

By  interest  on  500      from  Apr.24/95,toOct.  12/96,  171-  14    5 

By     do.        3  133  25 25 12,  ..170  316/ 

By     do.          29624     May       3 12,..    162  7  88 

By  do.    215    5 12,  ..1(50  5  65 

By  do.    215  SO  June  [) 12,  . .  125  4  43 

By  do.    109  74 24 12,  . .  110  2  0 

By     do.          51790     July     20 12,..      84  7  15 

Balance  due  on  this  account  carried  t«  the  debit  of  ac't.  143  3S 


dok   21621 


Sakntf  Sj€* 


Account  with  Thomas  Merchant  O. 

1799.  cloh.  cts,  dols,  cU. 

Jan  16,     By  interest  on         339  (>7 

427  81 

• I",    nf,    d, 

767  48    —  6    IS  25  32 

Balance  carried  to  account  current » • 417  21 


dols.    442  53 


Salc;n,  August  iGth,  \7^9. 

Errors  Excepted, 

THOMAS  MERCHANT, 


V     274-     ) 

CHARTER-PJRTF. 

THIS  Charter-party  of  afFreigbtment,  indented,  made  and  fully  conrlude^f 
upon  iliib  niiiih  day  of  June,  in  the  year  of  our  Lord,  one  thousand  ci'4it  hun- 
dred, between  J.  F.  of  Boston,  in  the  county  of  Suifolk,  and  Cornniirnweahh 
of  Massachusetts,  merchant,  owner  of  the  good  slnp  Ileltn,  of  the  burden  of 
two  liundred  tons,  or  thereabouts,  now  iying  in  tlie  harbour  of  Boston,  whereof 
II.  P.  is  at  pre>eiit  master,  on  the  one  part,  and  C.  D,  of  said  Boston,  mer- 
chant, on  liie  other  part,  iVityicsscth,  That  the  said  J.  P.  for  the  consideration 
liereaiter  mentioned,  hath  letlen  to  freight  tlie  aforesaid  bhip,  with  the  a|)pur- 
tenances  to  her  belonging,  tor  a  voyage  to  be  made  by  the  said  ship  to  Lon- 
don, wliere  sh.e  is  to  be  discharged  (ihe  danger  of  tlie  seas  excepted)  and  the 
said  J.  P.  dalii  by  these  presenis,  covciiant  and  agree  with  tlie  said  C  D.  in 
manner  foilowing.  That  is  lo  S'/y,  Tlial  the  said  ship  in  and  during  the  voyage 
aforesaid,  shall  be  tight,  staunch  and  strong,  and  sufTiciently  tackled  and  ap- 
paralled  with  all  things  necessary  for  such  a  vessel  and  voyage  ;  and  that  it 
shall  and  may  be  lawiul  lor  the  said  C.  D.  his  agent«  or  factors,  as  well  al 
London  as  at  Boston,  to  load  and  put  on  board  the  said  ship,  loading  of  such 
goods  and  merchandize  as  they  shall  think  pro])er,  contraband  goods  excepted. 

IN  consideration  wliereof,  the  said  C.  D.  doth  by  these  presents  agree  with 
the  said  J.  P.  well  and  truly  to  pay,  or  cause  to  be  paid,  unto  him,  in  full  for 
the  ireight  or  hire  of  said  ship  and  appurtenances,  the  sum  of  three  dollars 
per  ton,  per  calendar  month,  and  so  in  })r()portion  ior  a  Icss  time,  as  the  said 
ship  shall  he  co.itinued  in  !he  aforesaid  service,  in  sixty  days  after  her  return 
to  B;jston  And  the  said  C.  D.  d  :\h  agree  to  pay  llie  charge  of  victualing  and 
manning  said  ship  and  all  port  cliarges  and  pilotage  during  said  voya:;e,  and 
to  deliver  the  said  iliip  on  her  rct-,'>r:)  {^  B'.r'.cn,  to  (lie  owner  aforesaid  ;  r  his 
order.  And  to  the  true  and  faiihlul  of  all  and  singular  the  covenants,  |)ay- 
jnienls  and  a'^reemcn's  afore-mentiontxl,  eacli  of  the  p;u-t'es  arore-named  binds 
and  obliges  hnnseil,  his  executors  and  mid  admi.  i,4rators,  in  the  penal  sum  of 
two  [[(ousaiid  d'.;l!ari  hi  uily  by  these  presents.  In  witness  whereof,  the  par- 
ties afDresaid  have  hereunto  interchangeably  set  their  hands  and  seals  the  daj 
tiad  year  afore-writtcii." 


J.  R. 

1      a      o 

3 

Casks  Fot  / 

'hh. 

Inn      cir!. 

8        13       /. 

s. 

at    80s ;;;; 

12 

J^i  iini!i>^€  5 

|>r.   ct.        i 

15 

BILL  OF  LADING. 

SHIPPED  in  good  order  and  well  conditioiied  by  John 
Roily,  in  and  upon  th.e  g<i(;d  ship  called  the  Iris,  whereof 
is  master  Ibr  t!;is  prese,it  voyage  Charles  Ely,  and  no\y 
riding  at  anchor  in  the  harbour  of  Newport,  and  bound 
d.  for  i>iverj)oo!,  to  ^■dy,fj'tu-ihree  casks  of  pot  ash)  cojitaiu' 
0  i».^'  cii'-ht  /;)■.•>•  and  e}g!itccn  cu.t.  being  marked  and  num- 
be.d  as  in  fl'.c  niargii:,  and  are  to  be  delivered  in  l!  e  like 
7  go(.(l  order  iwA  well  coiiditioned,  at  the  afore-itid  ju  rt  of 
L;vc);;(».ji  (the  danger  of  the  seas  cxeepled  )  I'nto  ^Tr.  J. 


.f .    37      7    7    ^!;.y  or  kj  !iisa>:;<rnsJuM>rli!ev|)ay:ni2:  fieig!  1  :'.i  the  K("d 

goods.  Jour  pounds  Ihill^li  sU'iling  ptr  iou^  \s\ui  Uvv  per 

cent.  priuia,<:e.  in  witness  yvliereoij  the  master  or  pers'T 
oi'  ihe  said  ship  ha'h  afhrmed  lo  three  bills  oi  lading  all  of 
thic,  tenor  and  dale,  the  one  of  which  being  acc^uiplishc^i, 
the  other  two  to  stand  void.  Dated  at  Newport,  Julv  Til:^ 
IL^U.  C.  ELY. 


District  of  Massachusetts  District : 

. .  TO  WIT  : . . 

BE  IT  REMEMBERED,  That  on 

the  seventeenth  day  of  April,  in  the  twenty-fourth  year  of 
the  Independence  of  the  United  States  of  America, 
MICHAEL  WALSH,  of  the  said  District^  hath  deposited  in 
this  office,  the  title  of  a  Book,  the  right  whereof  he  claims 
as  Author,  in  the  words  following,  to  wit: 

^  A  X£W  SYSTEM  OF  MERCANTILE  AllITHMETIC: 
ADAPTED  TO  THE  COM.MERCE  OF  THE  UNITED  STATES, 
IN  ITS  DOMESTIC  AND  rOREIGN  RELATIONS;  WITH 
FORMS  OF  ACCOUNTS,  AND  OTII'eR  WRITINGS,  USUALLY 
OCCURRING   IN    TRADE BY   MICHAEL  WALSH.' 

In  conformity  to  the  Act  of  the  Congr^^s  of 

the  United  States,  intituled  "  An  Act  for  the  encourage- 
ment of  learning,  by  securing  the  copies  of  INIaps,  Qiart^ 
and  Books,  to  the  Authors  and  Proprietors  of  such  Copies, 
during  the  times  therein  mentioned." 

N.  GOODALE,  Clerk  of  the  District  of  Massachusetts  District 
A  true  copi/  of  record, 

Attest^^-^r—N.  GOODALE,  Clerk. 


PRINTING^ 

LeTTER-PRESS  <^^  COPPER.PLATE 
PRIISITING  executed  in  a  style  of  elegance 
and  on  reasonable  terms  at  the  Office  of 
Edmund  M.  Blunt,  State-Street,  Newbnry- 
port.  January,  1806. 


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